Question

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

(a) 37, 54

(b) 35.7, 40.7

(c) 50, 10

(d) 52.5, 7.5

This question was addressed to me during an online exam.

I'm obligated to ask this question of Trigonometric Ratios in section Trigonometry of Mathematics – Class 10

Answer 1

Correct option is (d) 52.5, 7.5

Explanation: The value of sin (A + B) = \(\frac {\sqrt {3}}{2}\) and sin 60° = \(\frac {\sqrt {3}}{2}\)

∴ A + B = 60      (1)

The value of tan (A – B) = 1 and tan 45° = 1

∴ A – B = 45     (2)

Adding equation (1) and (2)

A + B = 60

+ A – B = 45

– – – – – – – – – – – – –

2 A = 105

A = 52.5

∴ B = 7.5