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If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dot...

If `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+\ dotto\ oo)))` , prove that `(dy)/(dx)=(cosx)/(2y-1)`

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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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GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- MARCH 2015-SECTION-II
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