Verify the identity Simplify your answer completely 5 cos2 t

Verify the identity. Simplify your answer completely. 5 cos^2 theta - 5 sin^2 theta = 10 cos^2 theta = 5

Solution

5cos^2(B) - 5sin^2(B) = 10cos^2(B) - 5 (Verify)

LHS : 5cos^2B - 5(1- cos^2B)      ---->Trig identity : sin^2x +cos^2x =1

= 5cos^2B -5 +5cos^2B

= 10cos^2B -5