Question

ifcos 9a=sin a and 9a is greater then 90 degree then value of 5 a ​

Answer 1

Answer:

cos9α=sinα

⇒cos9α=cos(90°−α)

⇒9α=90°−α

⇒10α=90°

⇒α=9°

∴tan5α=tan45°=1

Hence, the answer is 1.

Answer 2

Answer :-

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

We have

Step-by-step explanation:

$A \:cos9A=sin \: A$

To find the value of

$tan 5A=?tan5A=? \\ </strong></p><p></p><p><strong>[tex] tan 5A=?tan5A=? \\ cos 9A=\sin (90-A)cos9A=sin(90−A)</strong></p><p></p><p><strong>[tex] tan 5A=?tan5A=? \\ cos 9A=\sin (90-A)cos9A=sin(90−A)$

$[ ∴\cos A= \sin (90-A)cosA=sin(90−A)</strong></p><p></p><p><strong>[tex][ ∴\cos A= \sin (90-A)cosA=sin(90−A)⇒ 9A = 90° - A</strong></p><p></p><p><strong>[tex][ ∴\cos A= \sin (90-A)cosA=sin(90−A)⇒ 9A = 90° - A⇒ 10 A = 90°</strong></p><p></p><p><strong>[tex][ ∴\cos A= \sin (90-A)cosA=sin(90−A)⇒ 9A = 90° - A⇒ 10 A = 90°⇒ A = \dfrac{90}{10}1090 = 9°</strong></p><p></p><p><strong>[tex][ ∴\cos A= \sin (90-A)cosA=sin(90−A)⇒ 9A = 90° - A⇒ 10 A = 90°⇒ A = \dfrac{90}{10}1090 = 9°∴ 5A = 5 × 9° = 45°</strong></p><p></p><p><strong>[tex][ ∴\cos A= \sin (90-A)cosA=sin(90−A)⇒ 9A = 90° - A⇒ 10 A = 90°⇒ A = \dfrac{90}{10}1090 = 9°∴ 5A = 5 × 9° = 45°$

$The \: value \: of \tan 5 \: Atan5 \: A = \tan 45tan \: 45 = 1</strong></p><p></p><p><strong>[tex]The \: value \: of \tan 5 \: Atan5 \: A = \tan 45tan \: 45 = 1$

[ ∴tan 45= 1tan 45 = 1

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