Question

If $3\Theta$ is an acute angle, solve the following equation $\Theta$:$(cosec3\Theta -2)(cot2\Theta -1)=0.$

Answer 1

We have,

$(\csc 3\theta -2)(\cot 2\theta -1)=0$

Either,

$\csc 3\theta -2=0$ or $\cot 2\theta -1$

$\csc 3\theta =2,\cot 2\theta =1$

$\csc 3\theta =\csc \frac{\pi }{6},\cot 2\theta =\cot \frac{\pi }{4}$

$3\theta =\frac{\pi }{6},2\theta =\frac{\pi }{4}$

$\theta =\frac{\pi }{18},\theta =\frac{\pi }{8}$

Hence, this is the answer.