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QUESTION 2Prove the identity: sin 0 + cos6 e + 3 sind e cos2 0 = 1.​

Answer»

Answer:

SIN4 θ – COS4 θ

= (sin2 θ)2 – (COS2 θ)2

= (sin2 θ – cos2 θ)(sin2 θ + cos2 θ)

= (sin2 θ – cos2 θ) × 1

= sin2 θ – cos2 θ = R.H.S.

= sin2 θ – (1 – sin2 θ)

= sin2 θ – 1 + sin2 θ

= 2 sin2 θ – 1 = R.H.S.

= 2(1 – cos2 θ) – 1

= 2 – 2 cos2 θ – 1

= 1 – 2 cos2 θ = R.H.S.

Hence PROVED.


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