1.

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

Answer»

Here, sin (A – B) = 1/2 

⇒ sin (A – B) = 30° [∵ sin 30° = 1/2 ] 

⇒ (A – B) = 30° …….(i) 

Also, cos (A + B) = 1/2 

⇒ cos (A + B) = cos 60° [∵ cos 60° = 1/2 ] 

⇒ A + B = 60° ….(ii) 

Solving (i) and (ii), we get: 

A = 45° and B = 15°



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