Question

If cos 9α = sin α and 9α < 90° then the value of tan 5α is

(a) $\frac{1}{\sqrt{3}}$

(b) $\sqrt{3}$

(c) 1

(d) 0

Answer 1

$$\begin{gathered} \cos 9\alpha =\sin \alpha \\ \Rightarrow \cos 9\alpha =\cos \left(90°-\alpha \right) \\ \Rightarrow 9\alpha =90°-\alpha \\ \Rightarrow 10\alpha =90° \end{gathered}$$
$$\begin{gathered} \Rightarrow 5\alpha =\frac{90°}{2}=45° \\ \therefore \tan 5\alpha =\tan 45°=1 \end{gathered}$$

Thus, the value of tan5α is 1.

Hence, the correct answer is option (c).