j-james/math

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All my math notes, now in Markdown.

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Prove Trig Identities

Learning Targets

You should be able to

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).