​ If y = x + tan x. Show that cos^2x . dy/dx = 2 – sin^2x ​

Question

If y = x + tan x. Show that cos²x . \(\frac{dy}{dx}\) = 2 – sin²x

Answer 1

Given y = x + tan x

\(\frac{dy}{dx}\) = 1 + sec²x = 1 + \(\frac{1}{cos^2x}\)

= \(\frac{cos^2x + 1}{cos^2x}\)

∴ cos²x\(\frac{dy}{dx}\) = cos²x + 1 = 1 – sin²x + 1 

= 2 – sin²x 

∴ cos²x \(\frac{dy}{dx}\) = 2 – sin²x