SOLUTION: Express in terms of the cosine function with exponent 1. cos^4 (theta/2) & sin^4 (2x) Show work please!!!

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Question 927300: Express in terms of the cosine function with exponent 1.
cos^4 (theta/2)
&
sin^4 (2x)
Show work please!!!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
cos%5E4%28theta%2F2%29+=cos%5E2%28theta%2F2%29+%2Acos%5E2%28theta%2F2%29 .....since cos%5E2%28theta%2F2%29+=%281%2F2%29+%28cos%28theta%29%2B1%29, we have



cos%5E4%28theta%2F2%29+=%281%2F4%29+%28cos%28theta%29%2B1%29%2A+%28cos%28theta%29%2B1%29



cos%5E4%28theta%2F2%29+=%281%2F4%29%28cos%5E2%28theta%29%2B2cos%28theta%29%2B1%29 .....since cos%5E2%28theta%29=%281%2F2%29%28cos%282+theta%29%2B1%29, we have









cos%5E4%28theta%2F2%29+=%281%2F8%29+%284cos%28theta%29%2Bcos%282theta%29%2B3%29%29




sin%5E4+%282x%29+=16+sin%5E4%28x%29+cos%5E4%28x%29 ...............=>sin%5E4%28x%29=+%281%2F8%29+%28-4+cos%282+x%29%2Bcos%284+x%29%2B3%29 and cos%5E4%28x%29=%281%2F8%29+%284+cos%282x%29%2Bcos%284x%29%2B3%29