Question

if sin (A+B) = under root 3/2 and sin (A-B)= 1/2 find A and B ​

Answer 1

Answer:

A = 45° and B = 15°

Step-by-step explanation:

sin (A + B) = √3/2 and sin (A - B) = 1/2

To find: value of A and B.

sin (A + B) = √3/2 and sin (A - B) = 1/2

sin (A + B) = sin 60° and sin (A - B) = sin 30°

As, sin 60° = √3/2 and sin 30° = 1/2

A + B = 60° and A - B = 30°

Add both the equation,

→ A + B + A - B = 60° + 30°

→ 2A = 90°

→ A = 45°

Substitute value of A in A+B=60°

→ 45° + B = 60°

→ B = 15°

Answer 2

=> sin (A+B) = √3/2

=> sin (A+B) = sin 60°

=> A + B = 60............Eq 1

=> sin (A-B) = 1/2

=> sin (A-B) = sin 30°

=> A - B = 30 .............Eq.2

solving eq.1 and eq.2

A + B = 60

A - B = 30

----------------

2B = 30

B = 15°

NOW from eq.2, A = 30 + 15 = 45°

therefore A = 45° and B = 15°