Question
Fri July 13, 2012 By:
 

If tan ? = 5 / 12 Find (1+cos ?)(1-cos ?)/(1+sin ?)(1 - sin ?)

Expert Reply
Sun July 15, 2012
Given : tanx = 5/12
to find : [(1+cos x)(1-cos x)] / [(1+sin x)(1 - sin x) ]
 
[(1+cos x)(1-cos x)] / [(1+sin x)(1 - sin x) ]
= ( 1- cos2 x ) / ( 1- sin2 x )                { using (a+b) (a-b) = a2 - b2  } 
=sin2x / cos2x                                      { using sin2 x + cos2 x = 1 }
= tan 2x                                                    { sin x / cos x = tan x }
= (5 2/122 )
= 25/144  answer 
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