SOLUTION: rewirte sin x^4 so that it involves only the first power of cosine..? stuck lol
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Question 618404: rewirte sin x^4 so that it involves only the first power of cosine..? stuck lol
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I presume you mean
)
Which is to say
\right)^4)
As opposed to
)
which is what you actually wrote.
Given that, write:
\ =\ \left(\sin^2(x)\right)\left(\sin^2(x)\right))
Then use the Pythagorean identity:
\right)\left(\sin^2(x)\right)\ =\ \left(1\ -\ \cos^2(x)\right)\left(1\ -\ \cos^2(x)\right))
Then use the difference of two squares factorization:
\right)\left(1\ -\ \cos^2(x)\right)\ =\ \left(1\ -\ \cos(x)\right)\left(1\ +\ \cos(x)\right)\left(1\ -\ \cos(x)\right)\left(1\ +\ \cos(x)\right))
Which is the desired result.
John
My calculator said it, I believe it, that settles it
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