Revision: 11th Std >> Trigonometry - II MAH-MHT CET (PCM/PCB) Trigonometry - II

L.H.S. = `(tan theta)/(sec theta - 1)`

= `(tan theta)/(sec theta - 1) xx (sec theta + 1)/(sec theta + 1)`

= `(tan theta  (sec theta + 1))/(sec^2 theta - 1)`  ...[a² - b² = (a + b)(a - b)]

= `(tan theta  (sec theta + 1))/(tan^2 theta)  ...[(1 + tan^2 theta = sec^2theta),(tan^2theta = sec^2theta - 1)]`

= `(cancel(tan theta)  (sec theta + 1))/(cancel(tan^2 theta)_(tan theta))`

= `(sec theta + 1)/(tan theta)`

L.H.S. = R.H.S.

Hence proved.