Question

tan theta = a/b then find Cost theta + sin theta / Cos theta - sin theta​

Answer 1

The value of$\frac { \cos \theta + \sin \theta } { \cos \theta - \sin \theta }$ is determined by dividing the numerator and denominator by \cos \thetacosθ

$\begin{gathered}\begin{array} { c } { \frac { \cos \theta + \sin \theta } { \cos \theta - \sin \theta } = \frac { \frac { \cos \theta } { \cos \theta } + \frac { \sin \theta } { \cos \theta } } { \frac { \cos \theta } { \cos \theta } - \frac { \sin \theta } { \cos \theta } } } \\\\ { = \frac { 1 + \tan \theta } { 1 - \tan \theta } } \end{array}\end{gathered}$

We know that $\tan \theta = \frac { \mathrm { a } } { \mathrm { b } }$

$\begin{gathered}\begin{aligned} & = \frac { 1 + \frac { \mathrm { a } } { \mathrm { b } } } { 1 - \frac { \mathrm { a } } { \mathrm { a } } } \\\\ & = \frac { \frac { \mathrm { b } + \mathrm { a } } { \mathrm { b } } } { \frac { \mathrm { b } - \mathrm { a } } { \mathrm { b } } } \\\\ = & \frac { \mathrm { b } + \mathrm { a } } { \mathrm { b } - \mathrm { a } } \\ \frac { \cos \theta + \sin \theta } { \cos \theta - \sin \theta } & = \frac { \mathrm { a } + \mathrm { b } } { \mathrm { b } - \mathrm { a } } \end{aligned}\end{gathered}$

Thus, the value of $\frac { \cos \theta + \sin \theta } { \cos \theta - \sin \theta } = \frac { a + b } { b - a }$