Question

$\cot \theta =\frac{7}{8}$, then evaluate $\frac{(1+\sin \theta )}{\cos \theta }$.

Answer 1

$\cot \theta =\frac{7}{8}\Rightarrow \tan \theta =\frac{8}{7}Then,\frac{1+\sin \theta }{\cos \theta }\Rightarrow \frac{1}{\cos \theta }+\frac{\sin \theta }{\cos \theta }Then,\Rightarrow \left(\sec \theta +\tan \theta \right)\Rightarrow \sqrt{1+{\tan }^2\theta }+\tan \theta \Rightarrow \left[\sqrt{1+{\left(\frac{8}{7}\right)}^2}+\frac{8}{7}\right]\Rightarrow \left[\sqrt{\frac{49+64}{49}}+\frac{8}{7}\right]=\frac{\sqrt{113}}{7}+\frac{8}{7}=\frac{\left(8+\sqrt{113}\right)}{7}$