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Question

5sinx-12cosx=-13sin3x,if =sin1(12/13), then

A
sin(2x-ϕ/2)=0
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B
sin(x+ϕ/2)=0
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C
cos(x+ϕ/2)=0
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D
cos(2x+ϕ/2)=0
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Solution

The correct option is A sin(2x-ϕ/2)=0
5sinx12cosx=13sin3x
513sinx1213cosx=sin3x sinϕ=1213
1213cosx513sinx=sin3x
sin(ϕx)=sin3x
sin(ϕx)sin3x=0
2cos(ϕx+3x2)sin(ϕx3x2)=0
2cosx(ϕ2+x)(sin(ϕ22x))=0
cos(ϕ2+x)=0 or sin(ϕ22x)=0

1210780_1338636_ans_1feaa6a99cb74634b7a9e89b7596dc0f.jpg

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