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Question

Find sin(A+BC) if
sin(B+C)=32
sin(A+C)=sin B and
sin A=12.


A

12

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B

32

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C

1

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D

12

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Solution

The correct option is B

32


Given,
sin(B+C)=32sin(A+C)=sin Bsin A=12

sin A=12,
A=30(1)

sin(B+C)=32
B+C=60(2)

sin(A+C)=sinB
A+C=B(3)

From the equations (1),(2) and (3)
C=60B, A=30
A+C=30+60B=B
2×B=90
B=45
B+C=60,C=6045
C=15
A+BC=30+4515=60
sin(A+BC)=sin 60=32


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