Help me on this one

Answer:

[tex]\displaystyle \frac{\cos x}{1 + \sin x} = \tan\left(\frac{\pi}{4} - \frac{x}{2}\right)[/tex].

Overview of the steps:

Step-by-step explanation:

Double-angle identity of sines and cosines:

Pythagorean identity for the sine and cosine of the same angle:

[tex]1 = \cos^2\alpha + \sin^2\alpha[/tex].

Angle sum and difference identity of sines and cosines:

[tex]\sin(\alpha - \beta) = \sin\alpha\, \cos\beta - \cos\alpha \, \sin\beta[/tex].

[tex]\cos(\alpha - \beta) = \cos\alpha\, \cos\beta + \sin\alpha \, \sin\beta[/tex].

Consider [tex]x[/tex] as the sum of two angles of size [tex](x/2)[/tex]. Start by applying the double-angle identity to the left-hand side.

[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\end{aligned}[/tex].

Apply the Pythagorean identity to rewrite the "1" in the denominator as [tex]\left(\cos^2(x / 2) + \sin^2(x / 2)\right)[/tex].

[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{\sin^2(x/2) + 2\,\sin(x/2)\, \cos(x/2) + \cos^2 (x/2)}\end{aligned}[/tex].

Note that the denominator is now a perfect square. On the other hand, the numerator is in the form [tex](x^2 - y^2)[/tex], which is equal to [tex](x + y)\, (x - y)[/tex]. Rewrite and simplify this expression:

[tex]\begin{aligned} \text{L.H.S.}&= \frac{\cos(x)}{1 + \sin(x)} \\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{1 + 2\, \sin(x / 2)\, \cos(x / 2)}\\ &= \frac{\cos^2(x / 2) - \sin^2(x / 2)}{\sin^2(x/2) + 2\,\sin(x/2)\, \cos(x/2) + \cos^2 (x/2)} \\[1em] &= \frac{(\cos(x/2) + \sin(x/2))\, (\cos(x/2) - \sin(x/2))}{\left(\sin(x/2) + \cos(x/2)\right)^2} \\ &= \frac{\cos(x/2) - \sin(x/2)}{\sin(x/2) + \cos(x/2)}\end{aligned}[/tex].

The tangent of an angle is equal to the ratio between its sine and its cosine. Apply the angle sum and difference identity of sine and cosine to the right-hand side.

Note, that the sine and cosine of [tex](\pi/4)[/tex] are both equal to [tex]\left(\sqrt{2}/2\right)[/tex].

[tex]\begin{aligned}\text{R.H.S.} &= \tan\left(\frac{\pi}{4} - \frac{x}{2}\right) \\ &= \frac{\sin((\pi/4) - (x/2))}{\cos((\pi/4) - (x/2))}\\ &= \frac{\left(\sqrt{2}/2\right)\, \cos(x/2) - \left(\sqrt{2}/2\right)\, \sin(x/2)}{\left(\sqrt{2}/2\right)\, \cos(x/2) + \left(\sqrt{2}/2\right)\, \sin(x/2)} \\ &= \frac{\cos(x/2) - \sin(x/2)}{\cos(x/2) + \sin(x/2)}\end{aligned}[/tex].

Therefore:

[tex]\displaystyle \text{L.H.S.} = \frac{\cos(x/2) - \sin(x/2)}{\sin(x/2) + \cos(x/2)} =\text{R.H.S.}[/tex].

[tex]\displaystyle \frac{\cos x}{1 + \sin x} = \tan\left(\frac{\pi}{4} - \frac{x}{2}\right)[/tex].

Answer:

-8 + i

Step-by-step explanation:

(-3 + 2i) * (2 + i)

= -6 + -3i + 4i + 2i^2

= -6 + i - 2

= -8 + i

Answer:

D. 3

Step-by-step explanation:

We can see from the graph that there are 3 lines. All 3 lines look linear, and if a line is linear, x and y are proportional. Therefore, if all 3 lines are linear, then we have 3 proportional relationships.

Answer:

[tex]\huge\boxed{\sf f = -4}[/tex]

Step-by-step explanation:

[tex]\sf -5f = 20\\\\Dividing\ both\ sides\ by\ -5\\\\\frac{-5f}{-5} = \frac{20}{-5} \\\\f = -4[/tex]

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

[tex]8x+9<4[/tex] and [tex]8x+9>-4[/tex].

Step-by-step explanation:

The given inequality is

[tex]|8x+9|<4[/tex]

We need to rewrite the given inequality as two linear inequalities.

We know that |8x+9|>0 but (8x+9) can be positive or negative.

For [tex]|8x+9|<4[/tex],  the value of (8x+9) must be lies between -4 and 4.

i.e., [tex]-4<8x+9<4[/tex]

If 8x+9 positive, then

[tex]8x+9<4[/tex]      ...(1)

If 8x+9 negative, then

[tex]8x+9>-4[/tex]      ...(2)

Therefore, the two inequalities are [tex]8x+9<4[/tex] and [tex]8x+9>-4[/tex].

Solution:

3[(8 - 4)^5] ÷ 8

3[4^5] ÷ 8

3[1024] ÷ 8

3072 ÷ 8

384

Best of Luck!

Answer:

384

Step-by-step explanation:

[tex]3[(8-4)^5][/tex]÷[tex]8[/tex]

Using the rules of PEMDAS I know that I have to do the math inside of the parenthesis first.

 8 - 4 = 4

Our new equation is

[tex]3[(4)^5][/tex]÷[tex]8[/tex]

Next we have to solve for the exponent.

[tex]4^5[/tex]  = [tex]4*4*4*4*4[/tex] = 1,204

Our new equation looks like:

[tex]3[1024][/tex]÷[tex]8[/tex]

Now we will multiply, because we follow the rules of operation.

[tex]3 *1024= 3072[/tex]

Finally we will divide 3,072 by 8.

[tex]3072/8= 384[/tex]

Our final answer is:

384

Answer:

g = 15/7

Step-by-step explanation:

3g - 9 + 11g - 21

group like terms

3g + 11g = 21 + 9

14g = 30

g = 30/14

g = 15/7

Answer:

200000+800000+0+2000+100+30+6

Step-by-step explanation:

2,000,000

800,000

0

2,000

100

30

+ 6

_________

Answer:

0.20613038098

Step-by-step explanation:

The formula for Binomial Probability =

P(X) =[ n!/(n - x)! × x! ] × p^x × q^n - x

From the question

x = 5

n = 15

p = 0.3

q = 1 - p

= 1 - 0.3 = 0.7

P(x = 5) = [15!/(15 - 5)! × 5! ] × 0.3^5 × 0.7^15 - 5

P(x = 5) = 3,003 × 0.3^5 × 0.7^10

P(x = 5) = 0.20613038098

Therefore, P(x = 5) = 0.20613038098

LM + MN = LN

5x + 5 = 11x - 1

Add 1 to both sides and subtract 5x from both sides

6 = 6x

Divide each side by 6

1 = x

MN = 5

LM = 5(1) = 5

LN = MN + LM = 5 + 5 = 10

Answer:

its A

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Answer:g(x)=-4^2+4x-5

Step-by-step explanation:

Answer:

Jacinta will have more money

Step-by-step explanation:

The interest amount is provided below for quarterly and daily compound:

Jacinta will have more money

Answer:

5.5

Step-by-step explanation:

divide the length value by 12

Answer:

5.5 ft

Step-by-step explanation:

30cm=1ft

12inch= 1ft

66/12 = 5.5ft

Answer:

REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEeeeeEEEEEEEEEEEEeeeeeee make sure you thank it.

Step-by-step explanation:

Step-by-step explanation:

55. 162 +54=216

216-75=141

balance $141

Answer:

3:4

Step-by-step explanation:

Answer:

  4 < 2a -4 < 10

Step-by-step explanation:

You have an expression for 'a'. To get an expression for 2a-4, multiply it by 2 and subtract 4.

  4 < a < 7

  8 < 2a < 14 . . . . . . multiply by 2

  4 < 2a -4 < 10 . . .  subtract 4

Answer:

S = { (4), (5), (1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (1,2,3,4), (1,2,3,5), (2,1,3,4) (2,1,3,5), (3,1,2,4), (3,1,2,5) }

A ={(4), (5)}

Step-by-step explanation:

Given that:

Among the three copies, (1,2,3) are the first printings, and (4,5) are the second printings.

A student who examines these books in random order stops when a second printing has been selected.

Thus, we can compute the sample space associated with these experiments as:

S = { (4), (5), (1,4), (1,5), (2,4), (2,5), (3,4), (3,5), (1,2,3,4), (1,2,3,5), (2,1,3,4) (2,1,3,5), (3,1,2,4), (3,1,2,5) }

Suppose A represents the event that we must examine exactly one book.

Then the outcomes of A are:

A ={(4), (5)}

Answer:  Each lemon costs 75 cents

Step-by-step explanation:

If you divide 8 from 6 then the answer is .75 and that is your answer.

Answer:

5 feet and 6 inches

Step-by-step explanation:

5 feet is 60 inches

Answer:

5 feet 6 inches

a foot is 12 inches. Go by 12s until you get to a number that's as close as you can make it without going overboard, then count what's left. 12 × 5 = 60, 66 - 60 = 6, hence 5 feet 6 inches

Answer:

M= D x V, V= M x D

Step-by-step explanation:

You just do the opposite of division since the original is:

Density= Mass/ Volume

Answer:

35 meters / minute.

Step-by-step explanation:

Speed of the leaf = 140 / 4 = 35 meters / minute.

Answer:

h(t) = 100(1.02)t + 20t + 10

Step-by-step explanation:

I got it right on the test : )

Answer:

h (t) = 100(1.02)t + 20t + 100

Step-by-step explanation: edge 2021

took the unit test got it right.

Answer:

1278.8 ft^3

Step-by-step explanation:

radius of cylinder = r = 5.8 ft

height of cylinder = h = 8.9 ft

radius of cone = r = 5.8 ft

height of cone = H - h = 18.5 ft - 8.9 ft = 9.6 ft

volume = volume of cylinder + volume of cone

V = (pi)(r^2)h + (1/3)(pi)(r^2)(H - h)

V = (3.14159)(5.8^2 ft^2)(8.9 ft) + (1/3)(3.14159)(5.8^2 ft^2)(9.6 ft)

V = 1278.8 ft^3

Answer:

If you use 3.14 for pi

1278.1 ft^2

Using the pi button on the calculator

1278.8 ft^2

Step-by-step explanation:

First find the volume of the cylinder

V = pi r^2 h where r is the radius and h is the height of the cylinder

V = pi ( 5.8) ^2 ( 8.9)

V = pi *33.64 * 8.9

V = 299.396 pi

The find the volume of the cone

V= 1/3 pi r^2h

The height of the cone is  18.5- 8.9 =9.6

V= 1/3 ( pi ) ( 5.8)^2 ( 9.6)

V= 1/3 ( pi ) 33.64 ( 9.6)

V = 107.648 pi

Add the two volumes together

299.396 pi + 107.648 pi

407.044 pi

If you use 3.14 for pi

1278.11816 ft^2

Rounding to the nearest tenth

1278.1 ft^2

Using the pi button on the calculator

1278.76644

Rounding to the nearest tenth

1278.8 ft^2

Answer:

What do u mean? For example, meters (works with other units of measurement) its based on an Acronym. King Henry Died By Drinking Chocolate Milk. The first letters stand for: Kilo, Hecto, Deca, Base (your unit of measurement), Deci, Centi, Mili

Step-by-step explanation:

Answer:

3 and 1 respectively.

Step-by-step explanation:

Subtract 3 from 4.

4 = 3 + x

4 - 3 = x

1 = x

Multiply 1 by 1.

The no. of pets friend has = 1