Question

16. If cos 9A = sin A and 9A < 90°, then find the value of tan 5A.


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Answer 1

Answer:

Here it is

Step-by-step explanation:

The value of \tan 5Atan5A is "1".

Step-by-step explanation:

We have,

\cos 9A=\sin Acos9A=sinA

To find, the value of \tan 5A=?tan5A=?

\cos 9A=\sin (90-A)cos9A=sin(90−A)

[ ∴\cos A= \sin (90-A)cosA=sin(90−A)

⇒ 9A = 90° - A

⇒ 10 A = 90°

⇒ A = \dfrac{90}{10}

10

90

= 9°

∴ 5A = 5 × 9° = 45°

The value of \tan 5Atan5A = \tan 45tan45 = 1

[ ∴\tan 45= 1tan45=1

Hence, the value of \tan 5Atan5A is "1