Question

Determine whethersecx cotx-cosxsin(-x) cot²xand cotx are equivalent. Justify your answer.

Answer 1

Person above is right

Answer 2

we have the expression

`(secxcot^2x-cosx)/(sin(-x)cot^2x)`

Rewrite the given expression

Remember that

sin(-x)=-sin(x)

`((1)/(cosx)(cos^2x)/(sin^2x)-cosx)/(-sinx(cos^(2)x)/(s\imaginaryI n^(2)x))`

Simplify the expression

`\begin{gathered} ((cosx)/(s\imaginaryI n^2x)-cosx)/(-(cos^2x)/(s\imaginaryI nx)) \\ \\ ((cosx-sin^2xcosx)/(sin^2x))/(-(cos^2x)/(sinx)) \\ \\ (cosx-s\imaginaryI n^(2)xcosx)/(s\imaginaryI n^(2)x)\colon-(cos^(2)x)/(s\imaginaryI nx) \\ \\ (sinx(cosx-sin^2xcosx))/(sin^2x(cos^2x)) \\ \\ ((cosx-sin^2xcosx))/(sin^x(cos^2x)) \\ \\ (cosx(1-s\imaginaryI n^2))/(s\imaginaryI nx(cos^2x)) \\ \\ ((1-s\imaginaryI n^2))/(s\imaginaryI nx(cosx)) \\ \\ (cos^2x)/(s\imaginaryI nx(cosx)) \\ \\ (cosx)/(sinx) \\ \\ cotx \end{gathered}`

therefore

The answer is

yes, the expression is equivalent to cot(x)