Question #26248

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Answer 1 · 2016-12-20T15:05:26

Given
#cosx+cosy=4/5#

#=>2cos((x+y)/2)cos((x-y)/2)=4/5........(1)#

Also given
#cosx-cosy=2/7#

#=>-2sin((x+y)/2)sin((x-y)/2)=2/7......(2)#

Dividing (2) by (1) we get

#-tan((x-y)/2)tan((x+y)/2)=2/7xx5/4#

#=>tan((x-y)/2))xx1/(cot((x+y)/2))=-5/14#

#=>14tan((x-y)/2))=-5(cot((x+y)/2))#

#=>14tan((x-y)/2))+5(cot((x+y)/2))=0#

Proved