Question

If ${\sin }^2\theta -2\sin \theta -1=0$ is to be satisfied for exactly 4 distinct values of $\theta \in [0,n\pi ],n\in N,$ then the least value of n is

• A. 2
• B. 6
• C. 4
• D. 15

Answer 1

The correct option is C 4

Here, $\sin \theta =1\pm \sqrt{2};$ but $|\sin \theta |\le 1.$ So,
$\sin x=1–\sqrt{2};$ which gives two values of $\theta$ in each of $[0,2\pi ],\left(2\pi 4\pi \right],(4\pi ,6\pi ]$, etc. Thus, the least value of
n =4.