Sum of Trigonometric Ratios in Terms of Their Product
If cos A+B si...
Question
If cos(A+B)sin(C−D)=cos(A−B)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 C0 Given, cos(A+B)sin(C−D)=cos(A−B)sin(C+D) ⇒cos(A−B)cos(A+B)=sin(C−D)sin(C+D)
By componendo and dividendo ⇒cos(A−B)+cos(A+B)cos(A−B)−cos(A+B)=sin(C−D)+sin(C+D)sin(C−D)−sin(C+D) ⇒2cosAcosB2sinAsinB=2sinCcosD−2cosCsinD ⇒cotAcotB=−tanCcotD ⇒tanAtanBtanC=−tanD ⇒tanAtanBtanC+tanD=0