Solve the inequality $$\frac{(2x-1)(x+2)}{x-\frac{\sqrt3}{2}}\leq0.$$[3] Hence solve, in exact form,

Question

Solve the inequality $$\frac{(2x-1)(x+2)}{x-\frac{\sqrt3}{2}}\leq0.$$[3] Hence solve, in exact form, $$\frac{(2\sin\theta-1)(\sin\theta+2)}{\sin\theta-\frac{\sqrt3}{2}}\leq0,\qquad 0\leq\theta\leq2\pi.$$[3]

Accepted Answer

(i) $x\in(-\infty,-2]\cup\left[\frac12,\frac{\sqrt3}{2}\right)$ (ii) $\theta\in\left[\frac{\pi}{6},\frac{\pi}{3}\right)\cup\left(\frac{2\pi}{3},\frac{5\pi}{6}\right]$

Sine substitution in a rational inequality

Sine substitution in a rational inequality

Video Solution:

Solution:

Solution locked