Question

Given $\sin \varphi =\frac{15}{17}$, find the value of : $\frac{3-4{\sin }^2\varphi }{4{\cos }^2\varphi -3}$

Answer 1

$\sin \varphi =\frac{15}{17}$

$\cos \varphi =\frac{\sqrt{{17}^2-{15}^2}}{17}=\frac{\sqrt{64}}{17}=\frac{8}{17}$

$\frac{3-4\times {\left(\frac{15}{17}\right)}^2}{4{\left(\frac{8}{17}\right)}^2-3}$

$\frac{3\times {17}^2-4\times {15}^2}{4\times 8^2-3\times {17}^2}=\frac{867-900}{256-867}=\frac{33}{611}$

$\therefore \frac{3-4{\sin }^2\varphi }{4{\cos }^2\varphi -3}=\frac{33}{611}$