Mathematics

Mathematics

Problem

Let θ\theta be an acute angle such that sin⁡θ=35\sin\theta=\dfrac{3}{5}. a. (i) Determine cos⁡θ\cos\theta and tan⁡θ\tan\theta. b. (ii) Find the exact values of sin⁡2θ,  cos⁡2θ\sin2\theta,\;\cos2\theta and tan⁡2θ\tan2\theta. c. (iii) Evaluate the expression P=sin⁡θ cos⁡2θ+cos⁡θ sin⁡2θP=\sin\theta\,\cos2\theta+\cos\theta\,\sin2\theta and simplify your answer.

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