Question 38

Mathematics Trigonometric Equations Hard

Solve the equation sin<sup>2</sup>&nbsp;x - sin x - 2 = 0, for x on the interval 0&nbsp;&le; x &lt; 2&pi;.

(A) <span class="math-tex">\(\dfrac{3\pi}{2}\)</span>
(B) <span class="math-tex">\(\dfrac{\pi}{4},\dfrac{2\pi}{7}\)</span>
(C) <span class="math-tex">\(\dfrac{2\pi}{3},\dfrac{2\pi}{5}\)</span>
(D) None of these
View Dynamic Solution & Explanation
Correct Solution: Option A

Step-by-step Solution:

Given that: \[ \sin^2 x - \sin x - 2 = 0 \] \[ \Rightarrow (\sin x - 2)(\sin x + 1) = 0 \] \[ \Rightarrow \sin x = -1 \] Hence: \[ x = \frac{3\pi}{2} \]