Question

Cos2a=2cos^2a-1=1-2sin^2a

Answer 1

Answer:

cos 2a = cos(a +a) = cos a . cos a - sin a . sin a = $cos^2 a - sin ^2a$

          (∵ cos(a+b) = cos a . cos b - sin a. sin b)

= $cos^2a - sin^2 a= 1 - sin^2 a -sin^2 a = 1 - 2 sin^2 a$

$1 - 2 sin^2 a = 1 - 2(1 - cos^2 a)\\= 1 - 2 + 2 cos^2a\\= 2cos^2a -1$

Hence Proved.