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Question

# The rate of change of the function$f(x)=\sin x+\csc x$ with respect to change in the variable $x$ is given by the expression $\cos x-\csc x\cot x.$ Show that the expression for the rate of change can also be $-\cos x\cot^2x.$

Solution

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Answered 2 years ago
Answered 2 years ago
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Work on the left side of the equation first by applying reciprocal identity for $\text{csc}x$, and quotient identity for $\text{cot}x$. So,

\begin{aligned} \text{cos}x-\frac{1}{\text{sin}x}\left(\frac{\text{cos}x}{\text{sin}x}\right) \end{aligned}

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