Prove that: sin4 θ – cos4 θ = 1 – 2cos2 θ - Vidyadip

Question

Prove that:
sin⁴ θ – cos⁴ θ = 1 – 2cos² θ

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Answer

L.H.S = sin⁴θ – cos⁴θ
= (sin²θ – cos²θ)(sin²θ + cos²θ)
= (sin²θ – cos²θ)
= (1 – cos²θ – cos²θ)
= 1- 2cos²θ

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