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