Question

If sin (A + B) = 1 and cos (A – B) = 1, 0° < A + B ≤90°, A ≥ B find A and B.

Answer 1

A = B = 45°

Step-by-step explanation:

Given: sin (A + B) = 1 and cos (A – B) = 1, 0° < A + B ≤90°, A ≥ B

Find: A and B

Solution:  

 sin (A + B) = 1  

 Sin 90° = 1

 So we get A + B = 90° -------(1)

 cos (A – B) = 1

 cos 0° = 1

 So we get A - B = 0° --------(2)

 Adding (1) & (2) = 2A = 90°

 Therefore A = 45°.

 Substituting in (1), we get 45° + B = 90°  

 Therefore B = 45°.