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Question

If cos(A+B)cos(A−B)+cos(C−D)cos(C+D)=0, then cotAcotBcotC is equal to

A
tanD
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B
cotD
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C
tanD
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D
cotD
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Solution

The correct option is C tanD

Given, cos(A+B)cos(AB)+cos(CD)cos(C+D)=0

[cos(A+B)=cosAcosBsinAsinB,cos(AB)=cosAcosB+sinAsinB]


1tanAtanB1+tanAtanB+1+tanCtanD1tanCtanD=0


2(1+tanAtanBtanCtanD)(1+tanAtanB)(1tanCtanD)=0


tanAtanBtanCtanD=1


cotAcotBcotC=tanD


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