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Question

If cos(A+B)=0 and sin(AB)=1/2, then find the value of A and B where A and B are actual angles.

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Solution

Given,
cos(A+B)=0 and sin(AB)=1/2

cos(A+B)=cos(90o) and sin(AB)=sin(30o)

Since A,B are acute

or, A+B=90o.....(1) and AB=30o......(2)

Solving from (1) and (2) we get,

A=60o and B=30o.

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