SOLUTION: Vertify is an identity cos^2(2x)+4sin^2(x).cos^2(x)=1

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Question 401384: Vertify is an identity
cos^2(2x)+4sin^2(x).cos^2(x)=1
Found 2 solutions by Tatiana_Stebko, richard1234:
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
%28cos%282x%29%29%5E2%2B4%28sinx%29%5E2%2A%28cosx%29%5E2=1
%28cos%282x%29%29%5E2%2B%282%2Asinx%2Acosx%29%5E2=1
Use FORMULA 2%2Asinx%2Acosx=sin%282x%29
%28cos%282x%29%29%5E2%2B%28sin%282x%29%29%5E2=1
Use FORMULA %28sinx%29%5E2%2B%28cosx%29%5E2=1, so %28sin%282x%29%29%5E2%2B%28cos%282x%29%29%5E2=1
1=1

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Btw, it's spelled "verify," not "vertify." I can immediately determine who wrote each problem based on the spelling...

Anyway, we can write 4%2Asin%5E2%28x%29cos%5E2%28x%29 as %282%2Asin%28x%29cos%28x%29%29%5E2. Applying double-angle formula for sine, this is equal to sin%5E2%282x%29. Therefore the expression is equal to

cos%5E2%282x%29+%2B+sin%5E2%282x%29, which is equal to 1 by the Pythagorean identity.