What is the tangent of csc(x) ?

The tangent of csc(x) is y=-cot(a_{0})csc(a_{0})x+csc(a_{0})+a_{0}cot(a_{0})csc(a_{0})

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tangent of csc(x)

tangent of

csc (x)

y = - cot (a_{0}) csc (a_{0}) x + csc (a_{0}) + a_{0} cot (a_{0}) csc (a_{0})

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, csc (a_{0}))

Find the slope of

y = csc (x) : \frac{d y}{d x} = - cot (x) csc (x)

Compute the slope of

y = csc (x)

x = a_{0} : m = - cot (a_{0}) csc (a_{0})

Find the line with slope m=

- cot (a_{0}) csc (a_{0})

and passing through

(a_{0}, csc (a_{0})) : y = - cot (a_{0}) csc (a_{0}) x + csc (a_{0}) + a_{0} cot (a_{0}) csc (a_{0})

y = - cot (a_{0}) csc (a_{0}) x + csc (a_{0}) + a_{0} cot (a_{0}) csc (a_{0})

y^{2} d x + x y d y = 0

x (3 x + 4)^{5}

y = (x^{2} - 2 x + 2) e^{x}

(x^{3} + 1)^{5}

\int 4 x^{3} + 9 x^{2} y^{2} + 3 d x

What is the tangent of csc(x) ?
The tangent of csc(x) is y=-cot(a_{0})csc(a_{0})x+csc(a_{0})+a_{0}cot(a_{0})csc(a_{0})