If sin (A + B) = \(\frac{\sqrt{3}}{2}\) and tan (A – B) = 1. What are the values of A and B ?

Question

Question

Answer 1

Formula used:

sin 60° = \(\frac{\sqrt{3}}{2}\)

tan 45° = 1

Calculation:

Given that,

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

⇒ sin (A + B) = sin 60°

∴ A + B = 60° ----(1)

Also, given

tan (A – B) = 1

⇒ tan (A – B) = tan 45°

∴ A – B = 45° ----(2)

Adding equation (1) and (2)

2 A = 105

⇒ A = 52.5

From equation (1), we will get

B = 7.5

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