Question

Please help! Prove - tan2x + sec2x = 1

Answer 1

Rewrite everything in terms of sine and cosine:

\[-\frac{\sin^2 x}{\cos^2 x}+\frac{1}{\cos^2 x} = 1\]

Then just add the fractions, and use the Pythagorean identity to show that it's true:

\[\frac{1-\sin^2 x}{\cos^2 x} = \frac{cos^2 x}{\cos^2 x} = 1\]

Answer 2

http://www.gradeamathhelp.com/image-files/trigonometric-identities-pythagorean.gif <--- notice the 2nd identity, solve for "1"