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Tan inverse (cosx/1+sinx)=π/4-x/2 prove this

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Tan inverse (cosx/1+sinx)=π/4-x/2 prove this

Posted by Mayank Pahuja 7 years, 11 months ago

CBSE > Class 12 > Mathematics

1 answers

Sandesh Verma 7 years, 11 months ago

LHS=tan^-1(cosx/1+sinx)=cos^2-sin^2/(cosx/2+sinx/2)^2 =tan^-1 (Cosx/2-sinx/2)(cosx/2+sinx/2) /(cosx/2+sinx/2)(cosx/2+sinx/2) =tan^-1(Cosx/2-sinx/2)/(cosx/2+sinx/2) =Cosx/2 common and cut it than =tan^-1(1-tanx/2)/(1+tanx/2) =tan^-1(tan(pi/4-x/2) =(Pi/4-x/2) Hence proved

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