Question #7083e

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Answer 1 · 2017-08-16T17:57:24

#sqrt(cot^(3)(x))#

We have: #frac(sqrt(cot(x)))(sin(x)) cdot cos(x)#

#= sqrt(cot(x)) cdot frac(cos(x))(sin(x))#

Let's apply the standard trigonometric identity #cot(x) = frac(cos(x))(sin(x))#:

#= cot^(frac(1)(2))(x) cdot cot(x)#

Using the laws of exponents:

#= cot^(frac(1)(2) + 1)(x)#

#= cot^(frac(3)(2))(x)#

#= sqrt(cot^(3)(x))#