Question Type 1: Solving trigonometric equations using reciprocal functions Exercises

Solve $\cot\left(\frac{x}{2}\right)=-1$ for $0<x<2\pi$.

Solve $4\sec x - 1 = 0$ for $0 \le x < 2\pi$.

Solve $\csc x = -\sqrt{2}$ for $0 \le x < 2\pi$.

Solve $\cot x = \sqrt{3}$ for $0 < x < \pi$.

Solve the equation $\sec \theta = 2$ for $0<\theta<2\pi$.

Solve $\sec(3x)=\tfrac{6}{\sqrt3}$ for $0<x<\tfrac{\pi}{2}$.

Solve $3\csc(2x) = -\sqrt{3}$ for $0 \le x < \pi$.

Solve the equation $\sec^2 x=4$ for $0<x<2\pi$.

Solve $2\cot x+\sqrt3=0$ for $0<x<\pi$.

Solve $2\sec x=4$ for $0\le x<2\pi$.

Solve $\text{cosec}\left(2x-\frac{\pi}{3}\right)=2$ for $0\le x<\pi$.

Solve $\csc\left(3x+\frac{\pi}{4}\right)=-2$ for $0 \le x < \pi$.