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If cot^-1 square root cos alpha - tan^-1 square root cos alpha = x , then sin x=?

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Solution:   We have ,      cot^-1sqrtcosalpha  -	an^-1sqrtcos alpha =x

               Rightarrow      fracpi2-	an^-1sqrtcos alpha-	an^-1sqrtcos alpha=x

                                             fracpi2-2	an^-1sqrtcos alpha=x

                  Taking sin on both the sides

              Rightarrow            sin (fracpi2-2	an^-1sqrtcos alpha)=sin x

             Rightarrow             cos (2	an^-1sqrtcos alpha )=sin x

             Hence        sin x=cos (2	an^-1sqrtcos alpha )=frac1-cosalpha1+cos alpha=	an^2fracalpha2.

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Deependra Verma

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