Question

Find the value of A if tan 4A = cot (A – 15°) where 4A and (A – 15°) are acute angles.

Answer 1

Given: tan 4A = cot (A – 15°) and 4A and (A – 15°) are acute angles.

Step-wise calculation:

1. Use cot x = tan (90° – x):

tan 4A = cot (A – 15°) 

= tan [90° – (A – 15°)] 

= tan (105° – A)

2. Since 4A and (A – 15°) are acute, 4A and 105° – A lie in (0°, 90°).

So, their principal tangent values must be equal without adding 180°: 4A = 105° – A.

3. Solve: 5A = 105°

⇒ A = 21°

4. Check angle ranges:

(A – 15°) = 6°   ...(acute)

4A = 84°   ...(acute)

Both conditions are satisfied.

A = 21°.