If y= root tan x + root tan x_+ root tan x + - Maths - Continuity and Differentiability

Question

If y= root tan x + root tan x_+ root tan x + to infinity, prove
that dy/dx = sec2 x/2y - 1

Ashok Kumar · Accepted Answer

y= root (tanx +y)
squaring both sides
y2 =tanx +y
y2- y =tanx
diff w r t x
2y dy/dx- dy/dx =sec2 x
(2y-1) dy/dx =sec2 x
dy/dx= sec2x/ ( 2y-1)

If y= root tan x + root tan x_+ root tan x + .......... to infinity, prove that dy/dx = sec2 x/2y - 1