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if tanx+sinx=m and tanx-sinx=n (m 2 -n 2 ) 2 is equal to

if tanx+sinx=m and tanx-sinx=n (m2-n2)2  is equal to

Grade:12th pass

1 Answers

Avinash
52 Points
4 years ago
Given m=tanx+sinx and n=tanx-sinx m^2=tan^2x+sin^2x+2sinx.tanxn^2=tan^2x+sin^2x-2sinxtanxm.n=tan^2x-sin^2x =sin^2x[1/cos^2x-1] =sin^2x[1-cos^2x/cos^2x] =sin^2x[sin^2x/cos^2x] =tan^2x.sin^2xAnd we know that m^2-n^2=4sinx.tanx [ m^2-n^2]^2=16sin^2x.tan^2x=16mnTherefore (m^2-n^2)^2=16mn

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