​If tan (3A) = cot (A - 22°), where 3A is an acute angle, then what is the value of A?​

Correct option is C

Given:

tan(3A) = cot(A - 22°), where 3A is an acute angle,

Solution:

cot(x) = tan(90° - x).

tan(3A) = tan(90°−(A−22°))

tan(3A) = tan(90°−A+22°)

tan(3A) = tan(112°−A)

Since the tangent function is periodic with a period of 180°, we have:

3A=112°−A+n⋅180°

where n is an integer. Since 3A is an acute angle, (i.e. (0^∘  < A < 90^∘).

3A = 112^∘- A

4A = 112^∘

A = 28^∘

∴ The correct answer is 28^∘.