Question

If sin(A+B)=1and sin(A-B)=1/2,0<_A=B<_90* and A>B. Then find A and B.

Answer 1

Sin (A+B) = 1
Sin (A+B) = sin 90°
A+B = 90° ------(1)

sin (A-B) = 1/2
sin (A-B) = sin 30°
A - B = 30° -------(2)

(1) + (2)
A+B+A-B = 90° + 30°
2A = 120°
A = 60°

A - B = 30°
60° - B = 30°
B = 60° - 30°
B = 30°

Therefore, A = 60° and B = 30°

Answer 2

★ TRIGONOMETRIC REDUCTIONS ★

Sin ( A + B ) = 1

A + B = 90° = π/2

Sin ( A - B ) = 1/2

A - B = 30° = π/6

Adding both the equivalents

2A = 120°

A = 60° = π/3

A + B = 90°

B = 30° = π/6

Therefore ,

HENCE , A = 60° or π/3 , B = 30° or π/6

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