What is sqrt(cos(x)csc^3(x)) ?

The solution to sqrt(cos(x)csc^3(x)) is csc(x)sqrt(cot(x))

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simplify sqrt(cos(x)csc^3(x))

simplify

cos (x) csc^{3} (x)

csc (x) cot (x)

Solution steps

cos (x) csc^{3} (x)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= cos (x) csc^{3} (x)

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= csc^{2} (x) csc^{1} (x) cos (x)

Apply radical rule:

a \cdot b = a b

= csc^{2} (x) csc^{1} (x) cos (x)

Apply radical rule:

assuming

a \geq 0

csc^{2} (x) = csc (x)

= csc (x) cos (x) csc^{1} (x)

Apply radical rule:

a b = a \cdot b,

assuming

a \geq 0, b \geq 0

cos (x) csc^{1} (x) = csc^{1} (x) cos (x)

= csc (x) csc^{1} (x) cos (x)

Apply rule

a^{1} = a

csc^{1} (x) = csc (x)

= csc (x) csc (x) cos (x)

csc (x) cos (x) = cot (x)

= cot (x) csc (x)

tan (θ + \frac{3 π}{2})

\frac{d y}{sin ^{2} ( y )}

cot (- 1 (x))

tan (arcsin (\frac{1}{x}))

sin (2 arctan (\frac{x}{4}))

What is sqrt(cos(x)csc^3(x)) ?
The solution to sqrt(cos(x)csc^3(x)) is csc(x)sqrt(cot(x))