Starting with the equation:
[tex]\frac{1}{\tan(x)}+\tan (x)=\frac{\sec ^2(x)}{\tan (x)}[/tex]Take the expression on the right hand side of the equation:
[tex]\frac{\sec ^2(x)}{\tan (x)}[/tex]From the Pythagorean Identity and the definition of secant, we can prove that:
[tex]1+\tan ^2(x)=\sec ^2(x)[/tex]That fact can be verified as follows: the Pythagorean Identity states that:
[tex]\sin ^2(x)+\cos ^2(x)=1[/tex]Divide both sides by the squared sine of x:
