Some Trig Identities

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Let’s remember a couple of trigonometric identities that are useful in integrating. How about the first one:

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

This is useful whenever we need to integrate \sin^2 x. Duh. The second, a close cousin, is

\displaystyle \cos^2 x = \frac{1+\cos 2x}{2}.

These are very similar, so you should learn them together. How are the different? (The plus/minus sign.) How can you tell which one is which? (Set x=0 and see which is equal to which.)

These two trig identities come up over and over in calculus and differential equations, so do yourself a favor and learn them today.