Question

# If $$y = \sqrt{\tan x+\sqrt{\tan x+\sqrt{\tan x+\cdots\text{to }\infty}}}$$, then $$\dfrac{dy}{dx} = \dfrac{p\sec^2 x}{qy+r}$$, $$p,q,r \in N$$. Find the minimum positive value of $$p+q+r$$.

Solution

## Square both sides the given equation, $$\Rightarrow y^2 = \tan x+y$$Now differentiate both sides with respect to $$x$$$$\Rightarrow 2y\dfrac{dy}{dx}=\sec^2x+\dfrac{dy}{dx}$$$$\Rightarrow (2y-1)\dfrac{dy}{dx}=\sec^2x$$$$\therefore \dfrac{dy}{dx}=\dfrac{\sec^2x}{2y-1}$$So, $$p=1, q = 2, r = -1$$$$\therefore p+q+r=2$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More