# 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,

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

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 11 Trigonometric Identities
Q 32 | Page 59