Let be an angle satisfying and .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let θ\theta be an angle satisfying sin⁡θ=35\sin\theta=\dfrac{3}{5} and π2<θ<π\dfrac{\pi}{2}<\theta<\pi. (i) Calculate cos⁡θ\cos\theta and tan⁡θ\tan\theta. Give exact values with correct signs. (ii) Compute sin⁡θ+cos⁡θ\sin\theta+\cos\theta and sin⁡θ tan⁡θ\sin\theta\,\tan\theta. (iii) Verify that (sin⁡θ+cos⁡θ)2+(sin⁡θ−cos⁡θ)2=2(\sin\theta+\cos\theta)^2+(\sin\theta-\cos\theta)^2=2 for this value of θ\theta. Present each step clearly.

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