Question

Find the smallest positive value of $\theta$ satisfying the equation $\sec 6\theta =\text{cosec}3\theta$.

Answer 1

$\sec 6\theta =co\sec 3\theta$
or $\sec 6\theta =\sec ({90}^0-3\theta )$
$\therefore 6\theta ={90}^0-3\theta$
or $9\theta ={90}^0$ or $\theta ={10}^0$