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Question

If cos(A+B)sin(CD)=cos(AB)sin(C+D), then the value of tanAtanBtanC+tanD is

A
2
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B
1
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C
0
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D
1
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Solution

The correct option is C 0
Given,
cos(A+B)sin(CD)=cos(AB)sin(C+D)
cos(AB)cos(A+B)=sin(CD)sin(C+D)

By componendo and dividendo
cos(AB)+cos(A+B)cos(AB)cos(A+B)=sin(CD)+sin(C+D)sin(CD)sin(C+D)
2cosAcosB2sinAsinB=2sinCcosD2cosCsinD
cotAcotB=tanCcotD
tanAtanBtanC=tanD
tanAtanBtanC+tanD=0

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