If Sin (A + B) = $$\frac{\sqrt3}{2}$$​ and cos (A – B) = $$\frac{\sqrt3}{2}$$​, then which of the following will be possible values of A and B?

Correct option is D

Given:

​$$\sin(A + B) = \frac{\sqrt{3}}{2}$$​

​$$\cos(A - B) = \frac{\sqrt{3}}{2}$$​

Solution:

​$$\sin(A + B) = \frac{\sqrt{3}}{2}$$ 

$$\sin(A + B) = sin \ 60 \degree$$ 

A + B = $$60 \degree$$  .........Equation (i)

​$$\cos(A - B) = \frac{\sqrt{3}}{2}$$ 

$$\cos(A - B) =cos\ 30 \degree$$ 

A - B = 30$$\degree$$  ........Equation (ii)

Add equation equation (i) and equation (ii)  

A + B + A - B = $$60 \degree + 30\degree$$ 

A = $$45\degree$$  

From equation (i) 

A + B = $$60 \degree$$ 

$$45\degree$$+ B =  $$60 \degree$$ 

B = $$15\degree$$​​

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