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If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ dotto oo)))`, prove that `(dy)/(dx)=(cosx)/(2y-1)` |
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Answer» Let ` y = sqrt(sin x + sqrt(sin x + sqrt(sin x + ............infty)))` ` y = sqrt(sin x + y ) ` Squaring both sides, we get, ` y^(2) = sin x + y ` Differentiating both sides, we get ` 2 y (dy)/(dx) = (dy)/(dx) + cos x ` ` (dy)/(dx) = (cos x)/((2y-1)) ` |
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