# j-james/math

All my math notes, now in Markdown.

View the Project on GitHub j-james/math

# Prove Trig Identities

## Learning Targets

You should be able to

• Verify / Prove (informally) trigonometric identities

## Concepts / Definitions

$\begin{matrix} \bold{Left-Hand-Side}&\ &\bold{Right-Hand-Side}\\ \cos{x}+\sin{x}\tan{x}&=&\sec{x}\\ \cos{x}+\frac{\sin{x}}{1}(\frac{\sin{x}}{\cos{x}})&=&\sec{x}\\ \cos{x}+\frac{\sin^2{x}}{\cos{x}}&=&\sec{x}\\ (\frac{\cos{x}}{\cos{x}})(\frac{\cos{x}}{1})+\frac{\sin^2{x}}{\cos{x}}&=&\sec{x}\\ \frac{\cos^2{x}}{\cos{x}}+\frac{\sin^2{x}}{\cos{x}}&=&\sec{x}\\ \frac{\sin^2{x}+\cos^2{x}}{\cos{x}}&=&\sec{x}\\ \frac{\sin^2{x}+\cos^2{x}}{\cos{x}}&=&\sec{x}\\ \frac{1}{\cos{x}}&=&\sec{x}\\ \sec{x}&=&\sec{x}\\ \end{matrix}$

To disprove an identity, you only need to show one particular example (like plugging in a number to show both sides are not equal).