​ If y = √(sin x+√(sin x+√(sin x....∞))) then dy/dx = ? ​A. sin x/(2y - 1) B. cos x/(y - 1) C. cos x/(2y - 1) D. none of these

Question

If y = \(\sqrt{sin\,x+\sqrt{sin\,x+\sqrt{sin\,x......\infty}}}\) then dy/dx = ?

√(sin x+√(sin x+√(sin x....∞)))

A. sin x/(2y - 1)

B. cos x/(y - 1)

C. cos x/(2y - 1)

D. none of these

Answer 1

Answer is: C. cos x/(2y - 1)

Given:

⇒ y = \(\sqrt{sin\,x+\sqrt{sin\,x+\sqrt{sin\,x+....\infty}}}\)

We can write it as

⇒ y = \(\sqrt{sin\,x+y}\)

Squaring we get

⇒ y² = sin x + y

Differentiating