Question

If cos 9α is equal to sin α and 9α < 90 then find the value of tan 5α

Answer 1

So, we know that

cos 9α= sin α

In order to find tan 5α we need to find α

so, we can use this

cos( 90-α) = sin α

Here, α= 9α

To,

sin (90-9α)= sin α

90- 9α= α

Transpose 9α to RHS

90= α+9α

90= 10α

$α=\frac{90}{10}$

Therefore, α=9

And tan 5α= tan 5 x 9= tan 45

tan 45° = 1

Answer 2

Heyy Buddy

Here's your Answer

Given :-

I am taking "a" in place of Alpha.

=> Cos 9a = sin a

we know that ,

cos ( 90 - a) = sin a.

=> Cos 9a = sin a can be written as

=> sin ( 90 - 9a) = sin a

=> 90 - 9a = a

=> 10a = 90

=> a = 9.

Now,

Value of tan 5a

Putting a = 9 here, we get

=> tan 5 × 9 = 45°

=> tan 45° = 1.
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