SOLUTION: Use the square identities to simplify 2(sin^2x)(sin^2x). {{{A.3+4cos(2x)+cos(4x)}}} {{{B.3-4cos(2x)+cos(4x)}}} {{{C.3-4cos(2x)-cos(4x)}}} {{{D.3+4cos(2x)-cos(4x)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Use the square identities to simplify 2(sin^2x)(sin^2x). {{{A.3+4cos(2x)+cos(4x)}}} {{{B.3-4cos(2x)+cos(4x)}}} {{{C.3-4cos(2x)-cos(4x)}}} {{{D.3+4cos(2x)-cos(4x)}}}       Log On


   

Question 930754: Use the square identities to simplify 2(sin^2x)(sin^2x).

A.3%2B4cos%282x%29%2Bcos%284x%29
B.3-4cos%282x%29%2Bcos%284x%29
C.3-4cos%282x%29-cos%284x%29
D.3%2B4cos%282x%29-cos%284x%29
Answer by rcdodds(6) About Me  (Show Source):
You can put this solution on YOUR website!
The trigonometric identity says that sin^2(x) = 1/2 - cos(2x)/2
Substituting this into the original equation and solving using trigonometric algebra gives us...
2%281%2F2+-+cos%282x%29%2F2%29%281%2F2+-+cos%282x%29%2F2%29
2%281%2F4-cos%282x%29%2F2%2B%28cos%5E2%282x%29%29%2F4%29
1%2F2-cos%282x%29%2B%28cos%5E2%282x%29%29%2F2
We also know from this identity that cos^2(2x)/2 = 1/4 + cos(4x)/4
1%2F2+-+cos%282x%29+%2B+1%2F4+%2B+cos%284x%29%2F4
3%2F4+-+cos%282x%29+%2B+cos%284x%29%2F4
3+-+4cos%282x%29+%2B+cos%284x%29
So we know that our answer is B