Question

If cos  \[9\theta\] = sin \[\theta\] and  \[9\theta\]  < 90⁰ , then the value of tan \[6 \theta\] is

Answer 1

It is given that,

\[\cos9\theta = \sin\theta, 9\theta < 90°\]
\[ \Rightarrow \sin\left( 90°- 9\theta \right) = \sin\theta \left[ \sin\left( 90° - \theta \right) = \cos\theta \right]\]
\[ \Rightarrow 90° - 9\theta = \theta\]
\[ \Rightarrow 10\theta = 90°\]
\[ \Rightarrow \theta = 9°\]
\[\text{ Therefore }, \tan6\theta = \tan54°.\]