Prove That: Sin4 θ + Cos4θ = 1 - 2sin2θ Cos2 θ.

Prove that: sin⁴θ + cos⁴θ = 1 - 2sin²θ cos²θ.

Sum

LHS = (sin²θ)² + (cos²θ)² + 2 sin²θ cos²θ - 2 sin²θ cos²θ

= ( sin²θ + cos²θ )²- 2 sin²θ cos²θ

= 1 - 2 sin²θ cos²θ

= RHS

Hence proved.

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Prove the following trigonometric identities.

tan²θ cos²θ = 1 − cos²θ

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Simplify

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cot θ . tan θ = ?

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