Verify the identity 2 sin2 x 1 1 2 cos2 x USe a pythagorean

Verify the identity.

2 sin² x 1 = 1 2 cos² x

USe a pythagorean identity and then simplify

Solution

2 sin^ 2 x - 1 = 1 - 2 cos^ 2 x

verifying the left hand side

2 sin^ 2 x - 1

1 can be written as sin^2 x + cos^2 x ( pythagorean identitiy )

therefore, 2 sin^2x - ( sin^2 x + cos^2 x )

sin^2 x - cos^2 x

again sin^2x = ( 1- cos^2 x )

( 1- cos^2 x - cos^2 x ) = 1 - 2 cos^2x ( which is our right hand side )

hence proved