Health High School

prove sinA*cos2A=1/4sin4A*secA
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Answers

Answer 1

Answer:

The prove is below

Explanation:

From trigonometric identities:

[tex]cos2A=cos(A+A)=cos^2A-sin^2A\\sin2A=sin(A+A)=2sinAcosA\\sin4A=sin(2A+2A)=2sin2Acos2A=2(2sinAcosA)(cos^2A-sin^2A)=4sinAcos^3A-4cosAsin^3A\\secA=\frac{1}{cosA}[/tex]

Therefore:

[tex]\frac{1}{4}sin4AsecA = \frac{1}{4}( 4sinAcos^3A-4cosAsin^3A)\frac{1}{cosA}\\= sinAcos^3A-cosAsin^3A(\frac{1}{cosA} )\\=sinAcos^2-sin^3A\\=sinA(cos^2A-sin^2A)\\But\ cos^2A-sin^2A=cos2A\\Therefore:sinA(cos^2A-sin^2A)=sinAcos2A\\\frac{1}{4}sin^4Acos2A=sinAcos2A[/tex]

Related Questions

A patient has a rash on his elbow, which is a(n)___symptom, especially compared to the deep ache that is caused by his arthritis.

Answers

Answer:

superficial

Explanation:

A patient has a rash on his elbow, which is a superficial symptom, especially compared to the deep ache that is caused by his arthritis.

What is a rash?

It is an area of skin that is irritated and may be swollen.

What is arthritis?

It is inflammation of joints that are also swollen.

Joint pain is most commonly associated with arthritis and is a physical symptom whereas the rash is associated with skin and is a superficial symptom

Is there arthritis that has a rash associated with it?

Yes, rheumatoid arthritis and psoriatic arthritis are the most common arthritis that has a rash associated with it.

To learn more about rash and arthritis here,

https://brainly.com/question/8311605

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Why do muscles become fatigued?

Answers

Answer:

Muscle fatigue. Muscle fatigue is the decline in ability of a muscle to generate force. It can be a result of vigorous exercise but abnormal fatigue may be caused by barriers to or interference with the different stages of muscle contraction.

What amount of alcohol can cause increase in apetite and help digestion

Answers

A Small amount, that’s what I could find. I don’t know the exact number so my bad for that

Which one of these grids is shaded red and blue in the ratio 1 : 1/3?
A
B.
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E
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Answers

Answer: A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."

Explanation:

 

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