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Trigonometric Ratios of Common Angles

Prove that co...

Question

Prove that $\frac{cos (π + x) cos (- x)}{sin (π - x) cos (\frac{π}{2} + x)} = {cot}^{2} x$

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Solution

$L . H . S . = \frac{cos (π + x) cos (- x)}{sin (π - x) cos (\frac{π}{2} + x)}$
$= \frac{(- cos x) cos x}{sin x (- sin x)}$
= $\frac{{cos}^{2} x}{{sin}^{2} x}$
= ${cot}^{2} x = R . H . S .$
Hence proved.

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Trigonometric Ratios of Common Angles

Standard XII Mathematics

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