Question

Sin(A-B)=1/2 and cos(A+B)=1/2 find A and B

Answer 1

Answer:

sin ( A - B ) = sin 30°

Cos ( A + B ) = cos 60°

( A - B) = 30° --> ( i ) , ( A + B ) = 60° --> ( ii )

Adding equation ( i) + ( ii )

2A = 90°

A = 45°

Putting value of A in ( i ),

45° - B = 30°

B = 45° - 30° = 15°

A = 45°, B = 15°

Answer 2

Sin(A-B) = Sin 30°

(A-B) = 30 (eq 1)

Cos (A+B) = Cos 60°

(A+B)= 60° ( eq 2 )

Asking both the equations

We will get A =45°

Put Value of A in eq 1 And we

will get B = 15°

Hope it helps :)