Question

Find acute angles A and B when 2 sin (A+B) = √3 and 2 cos (A-B) =√3.

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Answer 1

Answer:

sin(a+b)=√3/2=sin(60)

a+b=60

cos(a-b)=√3/2=cos(30)

a-b=30

solve the equations

a=45

b=15

all angle in degree

Answer 2

2sin(A + B) = √3

=> sin(A + B) = √3/2

We know that:

sin 60° = √3/2

Thus, A + B = 60 => A = 60 - B --(i)

2cos(A - B) = √3

=> cos(A - B) = √3/2

We know that:

cos 30° = √3/2

Thus, A - B = 30

Put (i)

=> 60 - B - B = 30

=> 30 = 2B

=> B = 15°

A = 60 - 15

=> A = 45°