Question

if theta=30° prove cos2theta=cos2theta-sin2theta

Answer 1

let us take rhs :

cos2∅-sin2∅

cos60-sin60

(∅=30° and 2∅= 60°)

½-√3/2

=1-√3/2

=1/2

(approximately)

=cos60°

=cos2(30)°

=cos2∅

hence proved.

Answer 2

@ = 30°

Cos2@ = cos2(30) = cos 60° = 1/2

cos 2@ - sin 2@ = cos 60° - sin 60°
= 1/2 - √3/2 = (1 - √3)/2 which is nearly equal to 1/2.

So LHS = RHS.

Hope This Helps You!