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Question
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
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Solution
It is given that,
\[\cos9\theta = \sin\theta, 9\theta < 90°\]
\[ \Rightarrow \sin\left( 90°- 9\theta \right) = \sin\theta \left[ \sin\left( 90° - \theta \right) = \cos\theta \right]\]
\[ \Rightarrow 90° - 9\theta = \theta\]
\[ \Rightarrow 10\theta = 90°\]
\[ \Rightarrow \theta = 9°\]
\[\text{ Therefore }, \tan6\theta = \tan54°.\]
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