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 (sin2x + 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.