Find all values of in satisfying .

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Find all values of θ\theta in 0≤θ<2π0\le\theta<2\pi satisfying sin⁡2θ=cos⁡θ\sin2\theta=\cos\theta. (a) θ=π6,7π6,5π6,11π6\theta=\dfrac{\pi}{6},\dfrac{7\pi}{6},\dfrac{5\pi}{6},\dfrac{11\pi}{6} (b) θ=π2,3π2\theta=\dfrac{\pi}{2},\dfrac{3\pi}{2} (c) θ=π6,π2,5π6,3π2\theta=\dfrac{\pi}{6},\dfrac{\pi}{2},\dfrac{5\pi}{6},\dfrac{3\pi}{2} (d) θ=π6,5π6\theta=\dfrac{\pi}{6},\dfrac{5\pi}{6}

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