Question Type 2: Solving more difficult trigonometric equations using reciprocal functions Exercises

Solve the equation $\sec^2 x - \tan^2 x = 3$ for $0 < x < \frac{\pi}{2}$.

Solve the equation $\cos x = \tan x$ for $0 < x < \pi$.

Solve the equation $\sin 2x = 2\cos x$ for $0 < x < \pi$.

Solve the equation $\sin x = \frac{1}{\sec x}$ for $0 \le x \le 2\pi$.

Solve the equation $\csc x - \sin x = 2$ for $0 < x < \pi$.

Solve the equation $3\sec x - 4\cos x = 0$ for $0 \le x < 2\pi$.

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

Solve the equation $4\sin2x = \pi\sec2x$ for $0 < x < \frac{\pi}{2}$.

Solve the equation $\sec x + \tan x = 2$ for $0 \le x < 2\pi$.

Solve the equation $\cot x + \tan x = 1$ for $0 < x < \frac{\pi}{2}$.

Solve the equation $2\csc x = \sin x$ for $0 < x < 2\pi$.

Solve the equation $\tan x = 3\csc x$ for $0 < x < \pi$.