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Question
If x = cosec A +cos A and y = cosec A – cos A then prove that `(2/(x+y))^2 + ((x-y)/2)^2` = 1
Solution
LHS = `(2/(x+y))^2 + ((x-y)/2)^2 - 1`
=`[2/((cosec A + cos A)+(cosec A - cos A))]^2 + [((cosecA+cosA)-(cosecA-cosA))/2]^2 - 1`
=`[2/(cosecA + cosA + cosecA-cosA)]^2 + [(cosecA +cosA-cosecA+cosA)/2]^2-1`
=`[2/(2cosecA)]^2 + [(2 cosA)/2]^2-1`
=`[1/(cosecA)]^2 + [cosA]^2-1`
=`[sinA]^2 + [cosA]^2-1`
=`sin^2 A + cos^2 A-1`
=1-1
=0
=RHS
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