A student attempts to solve by multiplying both sides by and obtains only the equation

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

Problem

A student attempts to solve

\sin\theta\,(1-2\sin\theta)=0

by multiplying both sides by

\csc\theta

and obtains only the equation

1-2\sin\theta=0

. Which of the following values of

\theta

0\le\theta<2\pi

is (are) missed by the student? (a)

\theta=\dfrac{\pi}{6},\dfrac{5\pi}{6}

(b)

\theta=0,\pi

(c)

\theta=0,\pi,2\pi

(d)

\theta=\dfrac{\pi}{2},\dfrac{3\pi}{2}