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  • If sin^-1 a=(alpha+beta) and sin^-1 b=(alpha-beta), then sin^2(alpha) +cos^2(beta) equals

If sin^-1 a=(alpha+beta) and sin^-1 b=(alpha-beta), then sin^2(alpha) +cos^2(beta) equals

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Solution:     a=sin(alpha +eta ) and b=sin(alpha -eta )

               We know that .

             Rightarrow     sin(alpha +eta )cdot sin(alpha -eta )=sin^2alpha -sin^2eta

            Rightarrow     sin^2alpha -(1-cos^2eta )

            Rightarrow      sin^2alpha +cos^2eta -1=ab

          Rightarrow      sin^2alpha +cos^2eta =1+ab

Posted by

Deependra Verma

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