Question Type 1: Finding solutions to equations using specific equalities and identities Exercises

Solve $\sin2x = 2\cos2x$ for $0 \le x \le \pi$.

Solve $2\sin2x = \pi\cos x$ for $0 < x < \frac{\pi}{2}$.

Solve $\sin 2x = \cos^2 x$ for $0 \le x \le \frac{\pi}{2}$.

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

Solve $2\sin 2x = \cos x$ for $0 \le x \le \frac{\pi}{2}$.

Solve $2\sin 2x + \sin x = 0$ for $0 \le x < 2\pi$.

Solve the equation $2\sin 2x = 3\pi \cos x$ for $0 < x < \pi$.

Solve $\sin2x - \cos2x = 1$ for $0 \le x < 2\pi$.

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

Solve $\sin2x = \cos x$ for $0 \le x < 2\pi$.

Solve $\sin 2x = \frac{\pi}{4}$ for $0 \le x < 2\pi$.

Solve $\cos2x + \sqrt{3}\,\sin x = 1$ for $0 \le x \le 2\pi$.