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

If Cos 9 θ = Sin θ and 9 θ < 900 , Then the Value of Tan 6 θ is - Mathematics

Sum

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

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

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Chapter 11: Trigonometric Identities [Page 59]

Q 32 Q 31 Q 33

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