Question

If A and B are acute angles such that sin(A+B)=1=cos(A-B),find A and B

Answer 1

Answer:

A = 45° , B = 45°

Step-by-step explanation:

Given A and B are acute angles.

i ) sin(A+B) = 1

=> sin(A+B) = sin90°

=> A+B = 90° ---(1)

ii) cos(A-B) = 1

=> cos(A-B) = cos 0°

=> A-B = 0° ---(2)

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

2A = 90

=> A = 45°

Substitute A = 45° in equation (1), we get

45° + B = 90°

=> B = 90° - 45°

=> B = 45°

Therefore,

A = 45° , B = 45°

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