Which of the following expressions is equivalent to $$\frac { 2 \cot ^ { 3 } t } { \csc t }$$ ? (a ? ?n,where n is a whole number) ? A)sin t (2 - 2 csc²t) B)cos t (2 csc²t - 2) C)cos t (2 - 2 csc²t) D)sin t (2 csc²t - 2) E)tan t (2 csc²t - 2)

Question

Quizplus · Accepted Answer

The given expression can be simplified using trigonometric identities. $\cot(t) = \frac{\cos(t)}{\sin(t)}$ and $\csc(t) = \frac{1}{\sin(t)}$. Substituting these into the original expression gives $\frac{2\cos^3(t)}{\sin^3(t)} \cdot \sin(t) = 2\cos^3(t) \cdot \frac{1}{\sin^2(t)} = 2\cos(t) \cdot \frac{\cos^2(t)}{\sin^2(t)}$. Using the identity $\csc^2(t) = 1 + \cot^2(t)$, we can rewrite the expression as $2\cos(t) \cdot (\csc^2(t) - 1)$, which simplifies to $2\cos(t) \cdot (\csc^2(t) - 1) = \cos(t) (2\csc^2(t) - 2)$, matching option B.

Which of the Following Expressions Is Equivalent To 2cot⁡3tcsc⁡t\frac { 2 \cot ^ { 3 } t } { \csc t }csct2cot3t​

Which of the Following Expressions Is Equivalent To $\frac { 2 \cot ^ { 3 } t } { \csc t }$