Question

Verify the trig identity 1/tan + tan= sec^2/ tan$\tan( \sec - \frac{\pi}{4} ) = \frac{ \tan( \sec( - 1) ) }{1 + \tan( \sec(?) ) }$

Answer 1

Starting with the equation:

$\frac{1}{\tan(x)}+\tan (x)=\frac{\sec ^2(x)}{\tan (x)}$

Take the expression on the right hand side of the equation:

$\frac{\sec ^2(x)}{\tan (x)}$

From the Pythagorean Identity and the definition of secant, we can prove that:

$1+\tan ^2(x)=\sec ^2(x)$

That fact can be verified as follows: the Pythagorean Identity states that:

$\sin ^2(x)+\cos ^2(x)=1$

Divide both sides by the squared sine of x: