Question

if tan 2A = cos (A-18 degree), where 2A is an acute angle ,find the value of A

Answer 1

Tan2A = cot(A - 18°) , where 2A is acute angle

We know, tan(90 - Ф) = cotФ , use it here
Tan2A = cot(90° - 2A)

∴ cot(90° - 2A ) = cot(A - 18°)
⇒ 90° - 2A = A - 18°
⇒ -2A - A = -90° -18°
⇒ - 3A = -108°
⇒A = 108° /3 = 36°

Hence, A = 36°

Answer 2

A correction in your question :

tan 2A = cot ( A - 18 )° , where 2A is an acute angle, Find A.

Angle 2A is an acute angle , Hence belongs to Quadrant 1 .

In Q1 , We have tanA = cot(90-A) .

We know that ,

90 - ( 90 - A+18) = 90 - 90 + A - 18 = A - 18

Here,



tan 2A = cot ( A - 18 )

tan 2A = cot [ 90 - ( 90- A + 18 ) ]

tan 2A = tan [ 90 - A + 18 ]

Cancelling Tangent on both sides ,

2A = 90 - A + 18

2A + A = 108

3A = 108

A = 36°

Therefore, 36° is the required answer.