Question

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

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Answer 1

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.