Krishna
0

Step 1:  Write the given ratios

            NOTE:   \cot \theta = \frac{b}{a}


            GIVEN: \frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta}


Step 2:  Calculate the values of the trigonometric ratios (sin & cos)

                           \frac{\cos \theta}{\sin \theta} = \frac{b}{a}

                                              If a^2 + b^2 = c^2 (Pythagoras theorem)

                         \frac{\cos \theta}{\sin \theta} = \frac{\frac{b}{c}}{\frac{a}{c}}


                            Cancel the c terms


                         \frac{\cos \theta}{\sin \theta} = \frac{b}{a}

                          Therefore \cos \theta = b \text{ and } \sin \theta = a


Step 2: Substitute the calculated values in the given equation


            GIVEN: = \frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta}


                         =   \frac{b + a}{b - a}