1.

Sin(A+B)=K and sin(A-B)=1/2;0

Answer»

Correct QUESTION:-

If sin(A + B) = 1 and sin (A-B) = 1/2, 0 ≤ A + B ≤ 90o and A > B, then find ∠A and ∠B.

Answer:-

GIVEN:

sin (A + B)° = 1

1 can be written as sin 90°.

So,

⟹ sin (A + B)° = sin 90°

On comparing both sides we get,

⟹ ∠A + ∠B = 90° -- equation (1)

SIMILARLY,

⟹ sin (A - B)° = 1/2

⟹ sin (A - B)° = sin 30°

⟹ ∠A - ∠B = 30° -- equation (2)

Add EQUATIONS (1) & (2).

⟹ ∠A + ∠B + ∠A - ∠B = 90° + 30°

⟹ 2∠A = 120°

⟹ ∠A = 120°/2

⟹ ∠A = 60°

Substitute the value of ∠A in equation (1)

⟹ ∠A + ∠B = 90°

⟹ 60° + ∠B = 90°

⟹ ∠B = 90° - 60°

⟹ ∠B = 30°


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