Question

If cos(A+B) =0 and sin(A-B) =1/2,then find the values of A and B, where A and B are acute angles.

Answer 1

cos(A+B)=0 and sin(A-B)=1/2

cos(A+B)=cos90 ( since value of cos 90 is 0)
then,
A+B=90 ( let it be equation 1)

Again,
sin(A-B)=1/2
sin(A-B)=sin30 (sice value of sin30 is 1/2)
then,
A-B=30. ( let it be equation 2)


Adding equation 1 and 2
A+B=90
A-B=30

2A=120
A=60
Now put the value of A in any of the equation either in 1 or in 2 ....let's put it in 1
then,A+B=90
60+B=90
B=30
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