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  • The derivative of tan^-1 (sin x / 1+cos x) w.r.t tan^-1 (cos x / 1+sin x ) is

The derivative of tan^-1 (sin x / 1+cos x) w.r.t tan^-1 (cos x / 1+sin x ) is

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Solution:   

              fracsin x1+cos x=frac2sin fracx2cdot cos fracx22cos ^2fracx2= an fracx2.

        Similarly ,       fraccos x1+sin x= an (fracpi4-fracx2).

        Let              u=tan^-1 an (fracx2)=fracx2

      And               v= an-1 an (fracpi4-fracx2)=(fracpi4-fracx2)

       herefore                fracmathrmd umathrmd v=-1.

Posted by

Deependra Verma

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