Question

If sin (A - B) =1/2, cos (A+B)=1/2,
0° < A + B > or =90°, A > B, find A and B.
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Answer 1

sin(A-B)=1/2=sin(30°)

so A-B=30

Cos(A+B)=1/2=cos(60°)

so A+B=60

A-B=30

adding the equations we get A+B+A-B=60+30

2A=90

A=45•

and A-B=30

so B=A-30=45-30=15°

Answer 2

A-B=30°

A+B=60

adding this two equations

A=45

and B=15°

Verified

0<45+15<90

Hope it helps

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