What is csc(arccos(1+3x)) ?

The solution to csc(arccos(1+3x)) is (sqrt(-9x^2-6x))/(-9x^2-6x)

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simplify csc(arccos(1+3x))

simplify

csc (arccos (1 + 3 x))

\frac{- 9 x ^{2} - 6 x}{- 9 x ^{2} - 6 x}

Solution steps

csc (arccos (1 + 3 x))

Use the following identity:

csc (arccos (x)) = \frac{1 - x ^{2}}{1 - x ^{2}}

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

Simplify

= \frac{- 9 x ^{2} - 6 x}{- 9 x ^{2} - 6 x}

- 4 π sin (10 π t - \frac{π}{3})

15 - 13 cos (10 x + π)

cos (x - \frac{5 π}{4})

sin^{2} (θ) - 1 + 2 cos (θ) sin (θ)

1 - sin^{2} (- x)

What is csc(arccos(1+3x)) ?
The solution to csc(arccos(1+3x)) is (sqrt(-9x^2-6x))/(-9x^2-6x)