Question

if cos (A-B)=√3/2 and sin (A-B) =1, then the value of A and B, respectively
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Answer 1

Correct Question:

If cos (A+B)=√3/2 and sin (A-B) =1, then the value of A and B, respectively

Reason: A - B = 60° & A - B = 90°

2A - 2B = 150° (which can't be solved)

Answer:

A = 75° and B = -15°

Step-by-step explanation:

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

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 90° = 1

A + B = 60° and A - B = 90°

Add both the equation,

→ A + B + A - B = 60° + 90°

→ 2A = 150°

→ A = 75°

Substitute value of A in A+B =60°

→ 75° + B = 60°

→ B = 60° - 75°

→ B = -15°