Question

How do you verify the trig identity :
sec x/csc squared x = sec x -cos x

Answer 1

http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.822716.html

Answer 2

Remember that \(\sec(x) = \frac{1}{\cos(x)}\) and \(\csc(x) = \frac{1}{\sin(x)}\)
So we can say:
$$
\frac{\sec(x)}{\csc^2(x)} = \frac{~~ \frac{1}{\cos(x)} ~~ }{ \frac{1}{\sin^2(x)} } = \frac{\sin^2(x)}{\cos(x)} = \\
= \frac{1 - \cos^2(x)}{\cos(x)} = \frac{1}{\cos(x)} - \frac{\cos^2(x)}{\cos(x)} = \sec(x) - \cos(x)
$$

Answer 3

Thank you so much for your guys help !

Answer 4

You're welcome =)