trig proofs

Oct 2008
23
1
I am having difficulty getting past the first step of solving this problem, can someone help me or check this for me? Thank you (Nod)

Original Problem: sin(x)^2 - sin(x)^4 = cos(x)^2 - cos(x)^4
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
I am having difficulty getting past the first step of solving this problem, can someone help me or check this for me? Thank you (Nod)

Original Problem: sin(x)^2 - sin(x)^4 = cos(x)^2 - cos(x)^4
\(\displaystyle \sin^2{x} - \sin^4{x} = \sin^2{x}(1 - \sin^2{x})\)

\(\displaystyle = \sin^2{x}\cos^2{x}\)

\(\displaystyle = (1 - \cos^2{x})\cos^2{x}\)

\(\displaystyle = \cos^2{x} - \cos^4{x}\).