#### Question

If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`

#### Solution

`x=cos^2θ and y=cot θ`

`(dx)/(dθ)=d/(dθ) (cos^2θ)`

`dx/(dθ)=-2cosθ sin θ`

`dy/dθ=-cosec^2θ`

`dy/dx=dy/(dθ)/dx/(dθ)`

= `(-cosec^2θ)/(-2cosθ sinθ)`

=`1/(2sin^3 θ cos θ)`

=`(1/2sin^3θ cos θ)θ=pi/4`

`(dy/dx)_θ=pi/4`

=`1/2(1/sqrt2)^3 1/sqrt2`

=`1/(2 1/4)=2`

Is there an error in this question or solution?

#### APPEARS IN

Solution If X = Cos2 θ and Y = Cot θ Then Find D Y D X a T θ = π 4 Concept: Increasing and Decreasing Functions.