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Properties Derived from Trigonometric Identities

If cosec27 ...

Question

If $c o s e c 27 = \frac{y}{x}$ then prove that $sec 27 - sin 63 = \frac{x^{2}}{y \sqrt{y^{2} - x^{2}}}$

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Solution

$sec 27 - sin 63 = sec 27 - cos 27$

$\Rightarrow \frac{1}{cos 27} - cos 27 = \frac{1 - {cos}^{2} 27}{cos 27}$

$\frac{\frac{x^{2}}{y^{2}}}{\sqrt{1 - \frac{x^{2}}{y^{2}}}} = \frac{x^{2}}{y \sqrt{y^{2} - x^{2}}}$

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Properties Derived from Trigonometric Identities

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