Question

If tan2A = cot(A-18°), where 2A is an acute angle. Find the value of A.

Answer 1

Tan 2A = cot ( A - 180
Tan 2A = tan ( 90- (A - 18))
Tan 2A = tan( 108 - A)
2A = 108 - A
3A = 108
Therefore
A = 36.

Answer 2

Heya,

Given=> tan2A = cot(A - 18°)

As we know that ,

Cot ( 90 - x ) = tan x

So, we will use same thing in question,

therefore,
Cot ( 90 - 2A ) = cot ( A - 18 )

Cancelling cot both sides, we get

=> 90 - 2A = A - 18
=> 3A = 108
=> A = 36°. ..... Answer

Hope this helps....:)