SOLUTION: Prove that 4(sin^4(x)+cos^4(x))=4-2sin^2(2x)

Algebra ->  Trigonometry-basics -> SOLUTION: Prove that 4(sin^4(x)+cos^4(x))=4-2sin^2(2x)      Log On


   

Question 1189605: Prove that 4(sin^4(x)+cos^4(x))=4-2sin^2(2x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Prove that 4(sin^4(x)+cos^4(x))=4-2sin^2(2x)
manipulate left side

4%28sin%5E4%28x%29%2Bcos%5E4%28x%29%29

=4%28sin%5E2%28x%29sin%5E2%28x%29+%2Bcos%5E2%28x%29cos%5E2%28x%29++%29

=4%28sin%5E2%28x%29%281-cos%5E2%28x%29%29+%2B%281-sin%5E2%28x%29%29cos%5E2%28x%29+%29+

=

=4%28sin%5E2%28x%29-2sin%5E2%28x%29cos%5E2%28x%29+%2Bcos%5E2%28x%29+%29 ..........sin%5E2%28x%29%2Bcos%5E2%28x%29=1

=4%281-2sin%5E2%28x%29cos%5E2%28x%29++%29 .............sin%5E2%28x%29cos%5E2%28x%29++=1%2F4+sin%5E2%282+x%29

=4%281-2%281%2F4%29+sin%5E2%282+x%29++%29+

=4-4%2A2%281%2F4%29+sin%5E2%282+x%29++%29+

=4-2sin%5E2%282x%29 -> proven