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 $x=frac{4 pi}{3}$