Question

If cos 9A= sin A and 9A<90 find the value of tan 5A

Answer 1

cos 9A = sin A 

cos 9A = cos (90-A) 

9A = 90 - A 

10A = 90 

A = 9 

So tan 5A = tan 45 = 1 

Answer 2

The value of $\tan 5A$ is "1".

Step-by-step explanation:

We have,

$\cos 9A=\sin A$

To find, the value of $\tan 5A=?$

$\cos 9A=\sin (90-A)$

[ ∴$\cos A= \sin (90-A)$]

⇒ 9A = 90° - A

⇒ 10 A = 90°

⇒ A = $\dfrac{90}{10}$ = 9°

∴ 5A = 5 × 9° = 45°

The value of $\tan 5A$ = $\tan 45$ = 1

[ ∴$\tan 45= 1$]

Hence, the value of $\tan 5A$ is "1".