Math, asked by darshu2229, 1 year ago

If x = tanA + sinA and y =tan A -sinA ,prove that: (x+y/x-y)^2 - (x+y/2)^2 =1

Answers

Answered by yogita8502
0

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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