Question

If sin(A-B)=1/2 and cos(A+ B)=1/2 then find A and B

Answer 1

Answer:

A = 45°, B = 15°

Step-by-step explanation:

$sin(A-B)=\frac{1}{2}$

$\implies sin(A-B)=sin30\degree$

$\implies A-B = 30\:--(1)$

$cos(A+B)=\frac{1}{2}$

$\implies cos(A+B)=cos60\degree$

$\implies A+B = 60\:--(2)$

/* Add equations (1) and (2) , we get

2A = 90°

=> A = 90°/2 = 45°

Substitute value of A in equation (2) ,we get

45° + B = 60°

=> B = 60° - 45°

=> B = 15°

Therefore,

A = 45°, B = 15°

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