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Question

If cos(xy)cos(x+y)+cos(7t)cos(7t)=0 then tan x tan y tan 7 tan t=


A

1

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B

-1

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C

2

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D

-2

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Solution

The correct option is B

-1


cos(xy)cos(x+y)+cos(7+t)cos(7t)=01tanxtany1tanxtany+1tan7tant1+tan7tant=0
(1+tan 7 tan t +tan x tan y +tan x tan y tan 7 tan t)+(1-tan 7 tan t-tan x tan y+tan x tan y tan 7 tan t)=0
2=-2 tan x tan y tan 7 tan t.
tan x tan y tan 7 tan t =-1.


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