Question

if y = 2-3 cosx /sin, find dy /dx at x= π/4​

Answer 1

6-2√2

Step-by-step explanation:

Consider y = (2-3 cos X) / sin X

y = 2/ sin x - 3 cos X / sin x

y = 2 cosec x - 3 cot x

Now differently we get

dy/dx=d/dx (3 cosec x- 3 cot x)

= 2 d/ dx ( cosec x - 3d/dx (cot x)

We know that d/ dx ( cosec x ) = - cosecx cot x

d/dx ( cotx)= - cosec^2 x

so. dy/dx = 2 ( - cosecx cotx - 3 ( - cosec^2 x)

= -2 cosec cot. x +3 cosec^2x

Now we need to put values that is x=Π\4 or 45 degree

dy/dx=- 2 cosec 45 cot 45+3 cosec^2 45

= -2√2x1+3x(√2)^2

= -2√2+2x3

So dy/dx=6-2√2