Sum

If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 90^{0} , then the value of tan \[6 \theta\] is

Advertisement Remove all ads

#### Solution

It is given that,

\[\cos9\theta = \sin\theta, 9\theta < 90°\]

\[ \Rightarrow \sin\left( 90°- 9\theta \right) = \sin\theta \left[ \sin\left( 90° - \theta \right) = \cos\theta \right]\]

\[ \Rightarrow 90° - 9\theta = \theta\]

\[ \Rightarrow 10\theta = 90°\]

\[ \Rightarrow \theta = 9°\]

\[\text{ Therefore }, \tan6\theta = \tan54°.\]

Concept: Trigonometric Identities

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads