Question

If $sin(A-B)=\frac{1}{2}$ and $cos(A+B)=\frac{1}{2}$, 0°

Answer 1

SOLUTION :

Given :  

sin (A - B) = ½ and cos (A + B) = 1/2

sin (A - B) = ½

sin (A - B) = sin 30°

[ sin 60° = ½]

A - B = 30° ………….(1)

cos (A + B) = 1/2

cos (A + B) = cos 60°

[Cos 60° = ½]

A + B = 60° …………..(2)

On adding eq 1 & 2,  

A + B = 60°

A – B = 30°

-----------------

2A  = 90°

A = 90°/2 = 45°

A = 45∘

On putting the value of  A = 45° in eq 2

A + B = 60°

45∘ + B =  60°

B = 60° - 45°

B = 15°

Hence, the value of A = 45° and B = 15°

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