Krishna
0

Step 1: Note down the given equation

            NOTE:   \cot \theta + \tan \theta = \sec \theta \cosec \theta


Step 2: Take the L.H.S of the equation and prove the R.H.S

            L.H.S: \cot \theta + \tan \theta

                    we can write this equation as following

                           \frac{\cos \theta}{\sin \theta} + \frac{\sin \theta}{\cos \theta}     


Step 3: Take the L.C.M

          EXAMPLE: =  \frac{\cos^2 \theta + \sin^2 \theta}{\cos \theta \sin \theta}


                              =     \frac{1}{\cos \theta \sin \theta}       (Since \cos^2 \theta + \sin^2 \theta = 1)


                             =     \frac{1}{\cos \theta}\frac{1}{\sin \theta}


                                        We know that   \frac{1}{\cos \theta} = \sec \theta

                                                                 \frac{1}{\sin \theta} = \cosec \theta


                              = So,   \sec \theta \cosec \theta