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