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Express tan^-1(cosx÷1-sinx);-π/2>x<π÷2 in the simplest form

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Express tan^-1(cosx÷1-sinx);-π/2>x<π÷2 in the simplest form

Posted by Jahanvi Sharma 7 years, 2 months ago

CBSE > Class 12 > Mathematics

1 answers

Sachinsingh Jatt 7 years, 2 months ago

=Tan inverse (cos²x/2-sin²x/2 ) sin²x/2+cos²x/2-2sinx/2 cosx/2) =Tan inverse(cosx/2+sinx/2)(cosx/2-sinx/2) (cosx/2-sinx/2)² =Tan inverse (cosx/2+sinx/2) (cosx/2-sinx/2) =Tan inverse(1+tanx/2) :-divided by cosx/2 (1-tanx/2) =Tan inverse (tan pi/4+tanx/2) : - tan pi/4=1 (1-tan pi/4 tanx/2) =Tan inverse tan(pi/4+x/2) =Pi/4+x/2

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