If sec 4A = cosec (3A - 50°), where 4A and 3A are acute angles, find the value of A + 75.

Explanation

Step 1: Use the Trigonometric Identity We know that: sec θ = cosec (90° - θ) In this problem, we have: sec 4A = cosec (3A - 50°) Therefore, we can write: 4A = 90° - (3A - 50°) Step 2: Solve for A Expanding and solving the equation: 4A = 90° - 3A + 50° 4A + 3A = 140° 7A = 140° A = 20° Step 3: Find A + 75 A + 75 = 20° + 75° = 95° Answer: The value of A + 75 is 95°.