Question

x=6cosec theta, y=8cot theta​

Answer 1

Answer:

Step-by-step explanation:

I hope you need the derivative of the both......

So it's derivative

dy/dx=4secx/3

Answer 2

Answer:

$\frac{dy}{dx}\ =\ \frac{4}{3}Sec\theta$

Step-by-step explanation:

In this question

We have been given that,

x = 6Cosecθ

y = 8Cotθ

We need to find the value of $\frac{dy}{dx}$

Since, y = 8cotθ

Therefore $\frac{dy}{d\theta}\ =\ -8Cosec^{2}\theta$

Similarly, x = 6 Cosecθ

$\frac{dx}{d\theta}\ =\ -6Cosec\theta cot\theta$

Therefore $\frac{dy}{dx}\ =\ \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$

$\frac{dy}{dx}\ =\ \frac{-8Cosec^{2}\theta}{-6 Cosec\thetaCot\theta}$

$\frac{dy}{dx}\ =\ \frac{4Cosec\theta}{3Cot\theta}$

On simplyfying further we get,

$\frac{dy}{dx}\ =\ \frac{4Sin\theta}{3Sin\thetaCos\theta}$

$\frac{dy}{dx}\ =\ \frac{4Sec\theta}{3}$

Therefore,$\frac{dy}{dx}\ =\ \frac{4Sec\theta}{3}$