Question

sin^2(75)-cos^2(75)=?

Answer 1

does this help? http://www.wolframalpha.com/input/?i=sin%5E2+75-cos%5E75%3D%3F

Answer 2

sin^2(theta) - cos^2(theta) = sin(2theta)

Answer 3

sin(2*75) = sin(150) = sin(90+60) = cos60

Answer 4

\[\cos 2\theta=\cos ^2\theta -\sin ^2 \theta \]
\[\sin ^2(75)-\cos ^2(75)=-\left( \cos ^2(75)-\sin ^2(75) \right)=-\cos (2*75)\]
\[=-\cos 150=-\cos \left( 180-30 \right)=-\left( -\cos 30 \right)=\cos 30=?\]