Question

If $cosec27=\frac{y}{x}$ then prove that $\sec 27-\sin 63=\frac{x^2}{y\sqrt{y^2-x^2}}$

Answer 1

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

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

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