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

Trigonometry (C10)
If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.

### Answer

Two angles are said to be complementary, if their sum is equal to 90°.

cot (90 - x) = tan x

According to the question,

tan 2A = cot (A - 18°)

cot (90 - 2A) = cot (A - 18°)

90 - 2A = A - 18°

3A = 108°

A = 36°