Find dy/dx given that y = 1 - cos x / sin x​

tan x

Step-by-step explanation:

The given function y is a quotient, so we must apply the quotient rule first.  Recall that (d/dx)cos x = -sin x and that (d/dx)sin x = cos x.

Then the derivative of the given quotient is:

              (sin x)[0 - (-sin x)]               [sin x]^2

dy/dx =       =   = 1

                     [sin x]^2                       [sin x]^2

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(-5,-28)

i graphed to on desmos.