If x = tanA + sinA and y =tan A -sinA ,prove that: (x+y/x-y)^2 - (x+y/2)^2 =1
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x-y=tanA+ sinA-tanA+sinA=2sinA
similarly,x+y =2tanA
then from the equation which we have to prove putting these values,
(2tanA/2sinA)^2-(2tanA/2)=1
now ,
tan^2A/sin^2A-tan^2A=1
tan^2A(1/sin^2A-1)=1
tan^2A(1-sin^2A)/sin^2A=1
As we know that:1-sin^2A=cos^2A
then ,
tan^2A×cos^2A/sin^2A=1
cos^2A/sin^2A=cot^2A
tan^2A×cot^2A=1
1=1
hence proved
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