Find all solutions of the equation in the interval .

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Find all solutions of the equation sin⁡2θ+cos⁡θ=0\sin 2\theta + \cos \theta = 0 in the interval 0≤θ<2π0 \le \theta < 2\pi. (i) Rewrite sin⁡2θ\sin 2\theta in terms of sin⁡θ\sin \theta and cos⁡θ\cos \theta, and simplify the given equation. (ii) Reduce the simplified expression to an algebraic equation in either sin⁡θ\sin \theta or cos⁡θ\cos \theta and solve for the trigonometric ratio(s). (iii) Hence determine all required values of θ\theta in the stated interval.

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