Solve the inequality $$\frac{(x-2)(x+1)}{x-1}\geq0.$$[3] Hence solve, in exact form, \[\frac{(\sec\t

Question

Solve the inequality $$\frac{(x-2)(x+1)}{x-1}\geq0.$$[3] Hence solve, in exact form, $$\frac{(\sec\theta-2)(\sec\theta+1)}{\sec\theta-1}\geq0,\qquad 0\leq\theta\leq2\pi,$$ where $\sec\theta$ is defined.[3]

Accepted Answer

(i) $x\in[-1,1)\cup[2,\infty)$ (ii) $\theta\in\left[\frac{\pi}{3},\frac{\pi}{2}\right)\cup\{\pi\}\cup\left(\frac{3\pi}{2},\frac{5\pi}{3}\right]$

Secant substitution in a rational inequality

Secant substitution in a rational inequality

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