Question

If cos 9 alpha is equals to sin alpha and 9 alpha is less than 90 degree find the value of tan 5 alpha

Answer 1

Given :

$\cos 9\alpha =\sin \alpha$

To find : $\tan 5\alpha$

Solution :

As we have given that

$\cos 9\alpha =\sin \alpha$

$\sin \alpha =\cos 9\alpha \\\\\cos (90-\alpha )=\cos 9\alpha\\\\90-\alpha=9\alpha\\\\90=9\alpha+\alpha\\\\90=10\alpha\\\\\dfrac{90}{10}=\alpha\\\\9=\alpha$

So, $\tan 5\alpha=\tan 5\times 9=\tan 45^\circ =1$

Hence, the required value is 1.