Question

If sin (A – B) =1/2 and cos (A + B) =1/2 , 0° < A + B ≤90°, A < B find A and B.

Answer 1

Step-by-step explanation:

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Answer 2

A = 45° ; B = 15°

Step-by-step explanation:

Given: If sin (A – B) =1/2 and cos (A + B) =1/2 , 0° < A + B ≤90°, A < B.

Find: A and B

Solution:  

 sin (A – B) = 1/2

  Sin 30° = 1/2

 So we get A - B = 30° -----------(1)

 cos (A + B) = 1/2

 Cos 60° = 1/2

 So we get A + B = 60° -----------(2)

Adding (1) & (2), we get: 2A = 90°

   Therefore A = 45°

Substituting A in (2), we get 45° + B = 60°  

    Therefore B = 15°