Mathematics

Mathematics

Problem

Simplify a higher-power trigonometric expression and apply it to a specific angle. a. (i) Prove that sin⁡4θ+cos⁡4θ=1−2sin⁡2θcos⁡2θ\sin^{4}\theta+\cos^{4}\theta=1-2\sin^{2}\theta\cos^{2}\theta for any acute angle θ\theta. b. (ii) Using θ=60∘\theta=60^{\circ}, determine the numerical value of sin⁡4θ+cos⁡4θ\sin^{4}\theta+\cos^{4}\theta.

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