Question

If tan5A = cot(4A – 18°) where 5A and (4A – 18°) are acute angles, what is the value of A?
1. 15° 
2. 12° 
3. 16° 
4. 18° 

Answer 1

Correct Answer - Option 2 : 12° 

Given:

tan5A = cot(4A – 18°)

Where 5A and (4A - 18°) are acute angles.

Concept:

tan(90° - A) = cotA

cot(90°- A) = tanA

Calculation:

tan5A = cot(4A – 18°)

⇒ cot(90° - 5A) = cot(4A - 18°)

⇒ 90° - 5A = 4A - 18°

⇒ 90°+ 18° = 4A + 5A

⇒ 108° = 9A

⇒ 12° = A

∴ The value of A is 12°