Step-by-step explanation:
Left-hand-side:
\displaystyle \dfrac{1}{sec(x) - tan(x)}
sec(x)−tan(x)
1
\displaystyle = \ \dfrac{1}{sec(x) - tan(x)} * \dfrac{sec(x) + tan(x)}{sec(x) + tan(x)}=
sec(x)−tan(x)
1
∗
sec(x)+tan(x)
sec(x)+tan(x)
\displaystyle = \ \dfrac{sec(x) + tan(x)}{sec^2(x) - tan^2(x)}=
sec
2
(x)−tan
2
(x)
sec(x)+tan(x)
Now use
\displaystyle 1 + tan^2(x) \ = \ sec^2(x)1+tan
2
(x) = sec
2
(x)
and you should be done.....
