What is csc(arccot(3x-4)) ?

The solution to csc(arccot(3x-4)) is sqrt(9x^2-24x+17)

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simplify csc(arccot(3x-4))

simplify

csc (arccot (3 x - 4))

9 x^{2} - 24 x + 17

Solution steps

csc (arccot (3 x - 4))

Use the following identity:

csc (arccot (x)) = 1 + x^{2}

= 1 + (3 x - 4)^{2}

Expand

1 + (3 x - 4)^{2} : 9 x^{2} - 24 x + 17

= 9 x^{2} - 24 x + 17

sin (π t + 2 π)

cos (- \frac{nπ}{2})

csc (arctan (\frac{4}{x}))

tan^{2} (\frac{π}{2} + x)

cos (\frac{π}{2} - \frac{π t}{2})

What is csc(arccot(3x-4)) ?
The solution to csc(arccot(3x-4)) is sqrt(9x^2-24x+17)