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Question

If sin(A+B)=32 and sin(AB)=12 when 0 < A, B < 90.
What is the value of A?

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Solution

Given,
sin(A+B)=32
And,
sin(AB)=12

We know that,
sin60=32
So, sin60=sin(A+B)
On comparing, A + B = 60 (i)

We also know that,
sin30=12
So, sin30=sin(AB)
On comparing, A - B = 30 (ii)

Add equation (i) and equation (ii),
(A + B) + (A - B) = 60 + 30
A + B + A - B = 90
2A = 90
A = 902
A = 45

Thus, A = 45

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