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Question

If sin(B+C)=32, sin(A+C)=sin B and sin A=12., then sin(A+BC) is .

A
1
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B
14
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C
34
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D
12
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Solution

The correct option is C 34
Given,
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=60B+30=B
2×B=90
B=45

Also, B+C=60
C=6045
C=15
A+BC=30+4515=60
sin(A+BC)=sin 60=32=34

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