Find the principal solutions of the following trigonometric equations.

Find the principal solutions of the following equations.

(i) $\cos x=\frac{1}{2}$

(ii) $\sin x=\frac{\sqrt{3}}{2}$

(iii) $\sec x=\frac{2}{\sqrt{3}}$

(iv) $\operatorname{cosec} x=2$

(v) $\cot x=\sqrt{3}$

(vi) $\tan x=\sqrt{3}$

sol Similar as Sample Question 1 of Concept $1 .$

Answer

(i) $x=\frac{\pi}{3}$ and $x=\frac{5 \pi}{3}$

(ii) $x=\frac{\pi}{3}$ and $x=\frac{2 \pi}{3}$

(iii) $x=\frac{\pi}{6}$ and $x=\frac{11 \pi}{6}$

(iv) $x=\frac{\pi}{6}$ and $x=\frac{5 \pi}{6}$

(v) $x=\frac{\pi}{6}$ and $x=\frac{7 \pi}{6}$

(vi) $x=\frac{\pi}{3}$ and $x=\frac{4 \pi}{3}$