Question

If $\cos 9\alpha =\sin \alpha$ and $9\alpha <{90}^o$, what is the value of $\tan 5\alpha$?

• A. $\frac{1}{\sqrt{2}}$
• B. $\sqrt{3}$
• C. $1$
• D. $\frac{1}{2}$

Answer 1

Answer: (C)

$1$

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

$\Rightarrow \cos 9\alpha =\cos (90°-\alpha )$

$\Rightarrow 9\alpha =90°-\alpha$

$\Rightarrow 10\alpha =90°$

$\Rightarrow \alpha =9°$

$\therefore \tan 5\alpha =\tan 45°=1$

Hence, the answer is $1.$