If x=cosec⁡θ−sin⁡θ,y=cosecn⁡θ−sinn⁡θthen(x2+4)(dydx)2−n2y2=

# If $x=\mathrm{cosec}\theta -\mathrm{sin}\theta ,y={\mathrm{cosec}}^{n}\theta -{\mathrm{sin}}^{n}\theta \text{then}\left({x}^{2}+4\right){\left(\frac{dy}{dx}\right)}^{2}-{n}^{2}{y}^{2}=$

1. A

${n}^{2}$

2. B

$2{n}^{2}$

3. C

$3{n}^{2}$

4. D

$4{n}^{2}$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

${x}^{2}+4=\left(\mathrm{cosec}\theta -\mathrm{sin}\theta {\right)}^{2}+4=\left(\mathrm{cosec}\theta +\mathrm{sin}\theta {\right)}^{2}$

$\left({x}^{2}+4\right){\left(\frac{dy}{dx}\right)}^{2}={n}^{2}\left({y}^{2}+4\right)⇒\left({x}^{2}+4\right){\left(\frac{dy}{dx}\right)}^{2}-{n}^{2}{y}^{2}=4{n}^{2}$

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formula Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)