devarshi-dt-logo

Question:

Let 2y = (cot⁻¹(√3cos x + sin xcos x - √3sin x))² then dydx is equal to

x - π/6

x + π/6

2x - π/6

2x - π/3

Solution:

Correct option is A. x - π/6
2y = (cot⁻¹(√3cos x + sin xcos x - √3sin x))²
2y = (cot⁻¹(√3 + tan x / 1 - √3tan x))²
2y = (cot⁻¹(tan(π/3 + x)))²
2y = (π/2 - cot⁻¹(tan(π/3 + x)))² = (π/2 - (π/3 + x))²
2y = (x - π/6)²
2y = x² - π/3x + π²/36
6y' = 2x - π/6