Question

if tan theta = a/b . find the value of cos theta +sin theta/cos theta-sin theta

Answer 1

Try understanding my writing.

Answer 2

Answer:

The result of $\frac { \cos \theta + \sin \theta } { \cos \theta - \sin \theta }$ is found out to be $\frac { \mathrm { a } + \mathrm { b } } { \mathrm { b } - \mathrm { a } }$

To find:

The result of $\frac { \cos \theta + \sin \theta } { \cos \theta - \sin \theta }$  when $\tan \theta = \frac { \mathrm { a } } { \mathrm { b } }$

Solution:

Given that the value of $\tan \theta = \frac { \mathrm { a } } { \mathrm { b } }$

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

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

We know that $\tan \theta = \frac { \mathrm { a } } { \mathrm { b } }$, as per the given question,

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

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