Question

If tan2A = cot (A-30) find A if 2A is an acute angel

Answer 1

Answer:

tan2A=tan(90-A+30)=tan120-A

2A+A=120

3A=120

A=40

Therefore the value of a is 40

Answer 2

Given :-

tan2A = cot(A - 30°) where 2A is an acute angle.

Here, we've to find the value of A.

tan 2A = cot(A - 30°) --------(i)

Also, tan 2A can be written as = cot(90° - 2A) --------(ii) [since cot(90 - ∅) = tan∅]

From equation (i) and (ii), we get

➡ cot(A - 30°) = cot(90° - 2A)

➡ A - 30° = 90° - 2A

➡ A + 2A = 90° + 30°

➡ 3A = 120°

➡ A = 120/3

➡ A = 40°

Hence, the value of A = 40°