Q: Value of the expression 2sinx – cos2x is

(A) greater than -3/2

(B) equal to – 3/2

(C) less than -3/2

(D) none of these

Sol. 2 sinx – cos2x = 2 (sin^{2}x + sinx) – 1

$\large = 2 [(sinx + \frac{1}{2})^2 – \frac{1}{4}] – 1 $

$\large = 2(sinx + \frac{1}{2})^2 – \frac{3}{2} \ge -\frac{3}{2}$

⇒ 2 sinx – cos2x ≥ – 3/2

Hence (A), (B) are the correct answers.