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Question
If y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ...... ∞)`, show that `("d"y)/("d"x) = (sin x)/(1 - 2y)`
Solution
y = `sqrt(cos x + sqrt(cos x + sqrt(cos x + ... ∞)`
∴ y2 = `cos x + sqrt(cos x + sqrt(cos x + ... ∞)`
∴ y2 = cos x + y
Differentiating w. r. t. x, we get
`2y ("d"y)/("d"x) = -sin x + ("d"y)/("d"x)`
∴ `("d"y)/("d"x)(1 - 2y)` = sin x
∴ `("d"y)/("d"x) = (sin x)/(1 - 2y)`
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