HSC Commerce 12th Board ExamMaharashtra State Board
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Solution for If X = Cos2 θ and Y = Cot θ Then Find D Y D X a T θ = π 4 - HSC Commerce 12th Board Exam - Mathematics and Statistics

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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`

 

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APPEARS IN

 2017-2018 (March) (with solutions)
Question 2.1.3 | 3.00 marks
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.
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