If sin (A - B) = 1/2 , and sin(A + B) = 1, where A and B are positive acute angles and A ≥ B, then A and B are respectively:

If sin (A - B) = 1/2 , and sin(A + B) = 1, where A and B…

If sin (A - B) = $\frac{1}{2}$ , and sin(A + B) = 1, where A and B are positive acute angles and A $\geq$ B, then A and B are respectively:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 60°, 30°.

Given that

Sin (A - B) = 1/2 = Sin 30º

⇒ A - B = 30º ......(1

Now,

Sin (A + B) = 1 = Sin 90º

⇒ A + B = 90º .......(2

Equation 1 + Equation 2

2A = 30 + 90 = 120°

⇒ A = 120°/2 = 60°

Put this value in Equation 2

60° + B = 90°

⇒ B = 90° - 60° = 30°