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

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## Answers

Answered by

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

Answered by

2

2sin(A + B) = √3

=> sin(A + B) = √3/2

We know that:

**sin**** ****6****0****°**** ****=**** ****√****3****/****2**

Thus, **A**** ****+**** ****B**** ****=**** ****6****0** => A = 60 - B --(i)

2cos(A - B) = √3

=> cos(A - B) = √3/2

We know that:

**cos 30° = √3/2**

Thus, **A**** ****-**** ****B**** ****=**** ****3****0**

Put (i)

=> 60 - B - B = 30

=> 30 = 2B

## => B = 15°

A = 60 - 15

## => A = 45°

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