Question

If $\tan 5\theta =\cot 4\theta .\sin {90}^o$. then find the value of $\cos 3\theta$.

Answer 1

Given,

$\tan 5\theta =\cot 4\theta .\sin {90}^o$

or, $\tan 5\theta =\tan ({90}^o-4\theta ).1$

or, $5\theta ={90}^o-4\theta$

or, $9\theta ={90}^o$

or, $\theta ={10}^o$.......(1).

Now

$\cos 3\theta$

$=\cos {30}^o$ [ Using (1)]

$=\frac{\sqrt{3}}{2}$.