Q. 15 I5.0( 1 Vote )

# Prove the following identities :cos4 θ – sin4 θ = cos2 θ – sin2 θ = 2 cos2 θ – 1

Given:

Taking I term

= cos4 θ – sin4 θ I term

= (cos2 θ)2 – (sin2 θ)2

= (cos2 θ – sin2 θ)(cos2 θ+ sin2 θ )

[ (a2 – b2) = (a + b) (a – b)]

= (cos2 θ – sin2 θ) (1) [ cos2 θ + sin2 θ = 1]

= (cos2 θ – sin2 θ) …(i) II term

From Eq. (i)

= {cos2 θ – (1 – cos2 θ)} [ cos2 θ + sin2 θ = 1]

= 2 cos2 θ – 1 III term

Hence, I = II = III

Hence Proved

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