O lvl A Maths: Trigonometric Identity

Prove the following trigonometric identity:

$\frac{cosec A - sin A}{sec A - cos A}\equiv \cot ^{3} A$

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Answer:

$\textup{LHS}= \frac{cosecA-sinA}{secA-cosA}$

$\large =\frac{\frac{1-\sin^{2}A}{\sin A}}{\frac{1-\cos^{2}A}{\cos A}}\large$

$\large =\frac{\frac{\cos^{2}A}{\sin A}}{\frac{\sin^{2}A}{\cos A}}$

$=\cot^{3} A=\textup{RHS (proved)}$

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O lvl A Maths: Trigonometric Identity