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  • The derivative of tan^-1 ( sin x / 1+cos x) with respect to tan^-1 [cos x /1+sinx]

The derivative of tan^-1 ( sin x / 1+cos x) with respect to tan^-1 [cos x /1+sinx]

Answers (1)

best_answer

Solution:   

              an^-1[fracsin x1+cos x]= an^-1[frac2sin fracx2cos fracx22cos^2fracx2]

Rightarrow                             = an^-1[ anfracx2]=fracx2

Now ,      an^-1[fraccos x1+sin x]= an^-1[fraccos^2fracx2-sin^2fracx2(cos fracx2+sin fracx2)^2]

Rightarrow                                  an^-1[ an(fracpi4-fracx2)]=fracpi4-fracx2

So , required answer is -1             

Posted by

Deependra Verma

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