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Question

If x=tanAāˆ’tanB,y=cotBāˆ’cotA then 1x+1y=

A
cot(AB)
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B
cot(BA)
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C
tan(AB)
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D
tan(BA)
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Solution

The correct option is D cot(BA)
tanAtanB=x,cotBcotA=y
We have tanAtanβ=x
=sin(AB)cosAcosB
cotBcotA=sin(AB)sinAsinB=y
1x+1y=cosAcosBsin(AB)+sinAsinBsin(AB)
=cosAcosB+sinAsinBsin(AB)=cos(AB)sin(AB)
1x+1y=cot(AB).

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