(a) Prove that for any integer and any real number , the following equalities hold:…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

(a) Prove that for any integer nn and any real number θ\theta, the following equalities hold: sin⁡(2nπ+θ)=sin⁡θandcos⁡(2nπ+θ)=cos⁡θ.\sin(2n\pi+\theta)=\sin\theta \quad \text{and} \quad \cos(2n\pi+\theta)=\cos\theta. (b) Using the result of part (a), simplify the expression A=sin⁡(468π+7π6)+cos⁡(−321π−4π3).A=\sin\left(468\pi+\dfrac{7\pi}{6}\right)+\cos\left(-321\pi-\dfrac{4\pi}{3}\right). (c) Hence find the exact value of AA.

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