(1-sin^2x) (1+tan^2x)=1
[tex]1 - sin {}^{2} x \times 1 + \tan( { }^{2} ) x = 1[/tex]
Prove that :
Please help i need the right one​

Answers

Answer 1

[tex]\tt (1 - sin ^2x)\times(1+tan^2x) = 1[/tex]

L.H.S

[tex]\tt cos^2x \times sec^2x[/tex]

[tex]\tt cos^2x \times \frac{1}{cos^2x}[/tex]

[tex]\tt \cancel{ cos^2x} \times\cancel{ \frac{1}{cos^2x}}[/tex]

[tex]\tt 1[/tex]

R.H.S

Hence proved

Answer 2

Step-by-step explanation:

[tex]{ \tt{ \blue{(1 - { \sin}^{2}x )(1 + { \tan }^{2}x) = 1 }}}[/tex]

• Remember → 1 + tan²x = sec²x

[tex] = { \tt{ \blue{(1 - { \sin }^{2}x)( { \sec}^{2}x) }}}[/tex]

• But sec²x → 1/cos²x

[tex] = { \tt{ \blue{(1 - { \sin}^{2} x)( \frac{1}{ \cos {}^{2} x} )}} }\\ \\ = { \blue {\tt{ \frac{1 - { \sin }^{2}x }{ { \cos }^{2}x } }}}[/tex]

• Remember from the first identity of trignometry;

[ cos²x + sin²x = 1 ].

• Therefore: [ cos²x = 1 - sin²x ]

[tex] = { \blue{\rm{ \frac{1 - { \sin}^{2}x }{1 - { \sin }^{2}x } }}} \\ \\ { \rm{ \blue{= 1 \: }}}[/tex]

Hence proved.


Related Questions

this graph represents the function f(x)=4sin(x) which statement is true about this function

Answers

Answer:

A

Step-by-step explanation:

The function is increasing in the interval in A because as the x-values increase so do the y-values on the graph, which can be shown by the graph sloping upwards at that specific section.

The graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given a graph of a trigonometric function,

As we know, the trigonometric function is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

From the graph, the function is increasing from 3π/2 to 2π

The graph slopes upward at that particular segment, indicating that the function is increasing in the interval in A as the x-values increase and the y-values on the graph follow suit.

Thus, the graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ5

I need help I don't understand this.

Answers

9514 1404 393

Answer:

  ∠4 = 108°

Step-by-step explanation:

Angles 2 and 4 together form a "linear pair". That is, the sum of them is 180°, a "straight angle." They are supplementary.

  ∠4 = 180° -∠2 = 180° -72°

  ∠4 = 108°

Mike has a total of 1371 coins in his piggy bank if the total value of his coins is $230.25 and make it only has dimes and quarters how many more times than quarters does Mike have

Answers

Answer:129

Step-by-step explanation:(621 x 0.25) + (750 x 0.10) = 230.25

750 - 621 = 129 more dimes than quarters

help me with this math question pls!! Find the value of x

Answers

Answer:

x = 3

Step-by-step explanation:

using the mid segment formula since quadrilateral WZYP is similar to that of MZYT, this is expressed as;

29 = 1/2(23 +11x+2)

Cross multiply

2(29) =  23+11x+2

58 = 25 + 11x

11x = 58 - 25

11x = 33

Divide both sides by 11

11x/11 = 33/11

x = 3

Hence the value of x is 3

SOMEONE HELP ME PLEASE
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.

There are 50 applicants for two Systems Engineer positions at a local company.

Answers

Answer:

you did not provide the numbers to answer any question...

but the formula that you want is probably this one

Combination Formula nCr=n!(n−r)!r!

Step-by-step explanation:

Which statement is true? O A. The number 23 is prime, but 36 is composite. B. The number 33 is prime, but 42 is composite. OC. The number 21 is prime, but 25 is composite. D. The number 27 is prime, but 39 is composite.​

Answers

Answer: A. The number 23 is prime, but 36 is composite.

=====================================================

Explanation:

Let's go through the possible answer choices

A) This is true because 23 only has the factors 1 and 23. So that's why 23 is prime. We can say 36 is composite since 2 is a factor, ie 36 = 2*18.B) This is false because 33 is not prime. Note how 33 = 3*11, showing that 3 is a factor of 33.C) Similar to B, the statement "21 is prime" is false. Note how 21 = 3*7.D) Like the other false statements, 27 is not prime because 27 = 3*9.

23 is indeed prime, and 36 is indeed composite.

33 is composite, and 42 is indeed composite.

21 is composite, and 25 is composite as well

27 is not prime, and 39 is composite.

Primes have only 2 factors: 1 and themselves.

And 33, 21 and 27 definitely have more than 2 factors. Hope this helps!

~Just a joyful teen

[tex]GraceRosalia[/tex]

Please answer this!!!!!!

Answers

Answer: 39°

Step-by-step explanation:

Angle of depression must be less than 90° but greater than 0°

find the slope of the tangent line of the curve r = cos (3theta) at theta = pi / 3

Answers

The slope of the tangent line to the curve at a point (x, y) is dy/dx. By the chain rule, this is equivalent to

dy/dθ × dθ/dx = (dy/dθ) / (dx/dθ)

where y = r(θ) sin(θ) and x = r(θ) cos(θ). Then

dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)

dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)

Given r(θ) = cos(3θ), we have

dr/dθ = -3 sin(3θ)

and so

dy/dx = (-3 sin(3θ) sin(θ) + cos(3θ) cos(θ)) / (-3 sin(3θ) cos(θ) - cos(3θ) sin(θ))

When θ = π/3, we end up with a slope of

dy/dx = (-3 sin(π) sin(π/3) + cos(π) cos(π/3)) / (-3 sin(π) cos(π/3) - cos(π) sin(π/3))

dy/dx = -cos(π/3) / sin(π/3)

dy/dx = -cot(π/3) = -1/√3

Find the missing side of triangle

Answers

Final Answer:

x = 20

Step-by-step explanation:

we'll be using the pythagorean theorem method, in this triangle the missing letter is a.

formula: [tex]a=\sqrt{c^2-b^2}[/tex]

a = x

b = 21

c = 29

a = [tex]\sqrt{29^2-21^2}[/tex]

a = [tex]\sqrt{841-441}[/tex]     (note: 29² = 29 × 29 = 841 and 21² = 21 × 21 = 441)

a = [tex]\sqrt{400}[/tex]

a = 20

x = 20

can she get some help

Answers

Answer:

-55

Step-by-step explanation:

the sqeuence seems to be subtracting by 2 everytime.

so it will be -1,-3,-5,-7,-9,-11,-13,-15,-17,-19,-21,-23,-25,-27,-29..

the answer will be 27*-2(-54) -1(because we start at -1 , not 0)

Answer:

Step-by-step explanation:

the formula for an arithmetic sequence that is explicit is

[tex]a_n=a_1+d(n-1)[/tex]  where [tex]a_1[/tex] is the first term (so -1), and d is the common difference (-2). n is the number position in the sequence. As soon as we find the formula or model for this sequence we can find any number term we want. Filling in the formula:

[tex]a_n=-1-2(n-1)[/tex] and we'll clean that up just a bit:

[tex]a_n=-1-2n+2[/tex] (I just distributed through the parenthesis) and a bit more to

[tex]a_n=-2n+1[/tex] and if we want the 21st term, fill in a 21 for n:

[tex]a_{21}=-2(21)+1[/tex] and

[tex]a_{21}=-42+1[/tex] so

[tex]a_{21}=-41[/tex]

Which of the following is the domain of the function based on the input-output table below?

Answers

Answer:

C

Step-by-step explanation:

The domain is the left side of the table

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah, a total of 8 people took the trip. She was able to purchase coach tickets for ​$300 and first-class tickets for ​$1060. She used her total budget for airfare for the​ trip, which was ​$6960. How many first-class tickets did she​ buy?
How many coach tickets did she​ buy?
number of first-class tickets bought nothing number of coach tickets bought nothing

Answers

Answer:

She bought 6 first class tickets and 1 coach ticket

Step-by-step explanation:

1060(6)= 6360 and 6960-6360=300 and 300 is the price for a coach ticket.

dleleleleldldldldlldldldldlddl

Answers

KILLER FISH KILLER FISH FROM SAN DIEGO

8
20
х
18
Solve for x.
O A) 40
B) 38
C) 45
D) 46

Answers

Answer:

its A

Step-by-step explanation:

A square has a perimeter of 80 m. What is the length of each side?

Answers

Answer:

20 m

[tex]p = 4a \: thus \: a = p \div 4 = 80 \div 4 = 20 \: m[/tex]

Answer:

20

Step-by-step explanation:

P=4L

80=4L

L=80/4

L=20m

for f(x)= -4x + 5, find f(x) when x = -2.

Answers

Answer:

13

Step-by-step explanation:

f(x)= -4x + 5

Let x = -2

f(-2) = -4(-2) +5

      = 8+5

     = 13

Step-by-step explanation:

x = - 2

f ( x ) = - 4x + 5

f ( - 2 )

= - 4 ( - 2 ) + 5

= 8 + 5

= 13

4x^2-12x+9.
4x^2+4x+1.,
1+12x+36^2

Answers

Answer:

Step-by-step explanation:

In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C

Answers

Answer:

90°

Step-by-step explanation:

Angle C = arccos((84²+13²-85²)/(2×84×13))

= arccos(0/2184)

= arccos(0)

= 90°

Answered by GAUTHMATH

Given the following coordinates complete the reflection transformation.​

Answers

Answer:

For a general point (x, y), a reflection across the line x = a transforms the point into:

(a + (a - x), y) = (2a - x, y)

So if we first do a reflection across the line x = 1, the new point will be:

(2*1 - x, y) = (2 - x, y)

And if we now do a reflection across the line x = 3, the new point will be:

(2*3 - (2 - x), y) = (6 - 2 + x, y) = (4 + x, y)

Now that we have the general formula we can solve the question.

For the point (-5, 2)

The generated point after the reflections is:

(4 + (-5), 2) = (-1, 2)

For the point (-1, 5)

The generated point after the reflections is:

(4 + (-1), 5) = (3, 5)

For the point (0, 3)

The generated point after the reflections is:

(4 +0, 3) = (4, 3)

what is the side length of the square in cm

Answers

Answer:

8.4 cm^2

Step-by-step explanation:

The area of the rectangle is

A = lw

A = 3x *5x = 15x^2

126 = 15x^2

126/ 15 =15x^2/15

42/5 = x^2

We want to find the area of the square

A = l*w

A = x*x

A = x^2 = 42/5 = 8.4 cm^2

The Cave of Swallows is a natural open-air pit cave in the state of San Luis Potosí, Mexico. The 1220-foot-deep cave was a popular destination for BASE jumpers. The function 1/4sqrt(d) represents the time t (in seconds) that it takes a BASE jumper to fall d feet. How far does a BASE jumper fall in 3 seconds? Pls answer this as quickly as possible. Thanks.

Answers

Answer:

The depth to which a BASE jumper jumps in 3 seconds is 144 feet

Step-by-step explanation:

The details of the Cave of Swallows are;

The depth of the cave = 1,220 ft.

The function that represents the duration, t, in seconds it takes to fall d feet is given as follows;

[tex]t = \dfrac{1}{4} \cdot\sqrt{d}[/tex]

The distance a BASE jumper jumps in 3 seconds = Required

By substituting t = 3 in the given function, we get;

[tex]t = 3 = \dfrac{1}{4} \cdot\sqrt{d}[/tex]

Therefore;

4 × 3 = 12 = √d

d = 12² = 144

The distance a BASE jumper jumps in 3 seconds is d = 144 feet.

Chase buys a bag of cookies that contains 6 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 6 oatmeal cookies. What is the probability that Chase randomly selects a peanut butter cookie from the bag, eats it, then randomly selects a chocolate chip cookie

Answers

Answer:

0.0652173

Step-by-step explanation:

Given that :

6 chocolate chip cookies

6 peanut butter cookies

6 sugar cookies

6 oatmeal cookies

Total number of cookies purchased = (6+6+6+6) = 24

Probability, P= required outcome /total possible outcomes

This is a selection without replacement probability problem :

P(peanut butter cookies) = 6/24 = 1/4

Then ;

P(chocolate chip cookie) = 6/23

Hence,

P(peanut butter cookies then chocolate chip cookie) = 1/4 * 6/23 = 0.0652173

Consider the following function.



Place the steps for finding f -1(x) in the correct order.
















Answers

Answer:

if f(x) = ax + b then f-1(x) = (x - b)/a

Step-by-step explanation:

Now

f(x)=ax + b

then y = ax + b

interchanging x and y , we get

or, x = ay + b

or, x - b = ay

or, (x - b)/a = y

therefore,f-1(x) = (x - b)/a

Which algebraic expression represents the phrase "six less than a number"?

Answers

Answer:

[tex]x-6[/tex]

Step-by-step explanation:

We can let the 'number' in the expression be equal to [tex]x[/tex]. Something 6 less than x would x minus 6, or [tex]x-6[/tex].

Answer:

x-6

Step-by-step explanation:

Let the number be x

Less than means subtract from

x-6

3+3+3+3+3+3+3+333333

Answers

Answer:

333354

Step-by-step explanation:

Simplify the expression.

Answer:

333,354

Step-by-step explanation:

First, we add the 3's. And get 21.

333,333 + 21 = 333,354

Need help asap, thanks :)

Answers

Answer:

937

425

Step-by-step explanation:

9 is the square of 3

7 is 1 more than 6, the double of 3

4 is the square of 2

5 is 1 more than 4, 2x 2

Is there more?

Answer:

425

Step-by-step explanation:

1st = 2^2

3rd = 2*2 + 1

What is the sum of the polynomials?

(7x3 – 4x2) + (2x3 – 4x2)


9x3 – 8x2

5x3

5x3 – 8x2

9x3

Answers

Answer:

9x3 - 8x2

Step-by-step explanation:

7x3+2x3 = 9x3

-4x2+(-4x2) = -8x2

Answer:

D

Step-by-step explanation:

10 • 4/10y = -28 • 10

Answers

Answer:

y=-70

Step-by-step explanation:

10.4/10y=-28.10

4y=-280

y=-70

Please help me solve this I’m really struggling

Answers

Answer:

y =x^2 +8x +15

factories form

y =( x+5 )( x+3 )

x intercept where the graph meet the x axis

y = x^2 +8x +15

let y =0

0 = x^2 +8x +15

0 = ( x + 5) (x+3)

o = x+5 or 0 = x+3

-5 = x or x = - 3

x intercept

(-5;0)

(-3 ;0)

axis of symmetry : where you will cut the graph into two half

x = - b/2a

x = - 8/2(1)

x = - 8/2

x = - 4

Domain

XER

Range

y > -1

Is the following number rational or irrational?
-117
Choose 1 answer:
Rational
Irrational

Answers

Answer:

-117 is irrational number

Answer:

Irrational

Step-by-step explanation:

Irrational number can't be written as a faction, -11pie can't be written as a fraction. Therefore it is a irrational number.

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