Mathematics

Mathematics

Problem

A student attempts to solve sin⁡θ (1−2sin⁡θ)=0 \sin\theta\,(1-2\sin\theta)=0 by multiplying both sides by csc⁡θ\csc\theta and obtains only the equation 1−2sin⁡θ=01-2\sin\theta=0. Which of the following values of θ\theta in 0≤θ<2π0\le\theta<2\pi is (are) missed by the student? a) θ=π6,5π6\theta=\dfrac{\pi}{6},\dfrac{5\pi}{6} b) θ=0,π\theta=0,\pi c) θ=0,π,2π\theta=0,\pi,2\pi d) θ=π2,3π2\theta=\dfrac{\pi}{2},\dfrac{3\pi}{2}

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