Basic formulas: sum and difference of arguments, double angle

Sum and difference of arguments

Addition formulas connect $\sin(\alpha\pm\beta)$ , $\cos(\alpha\pm\beta)$ and $\tan(\alpha\pm\beta)$ (where the last is defined) with the sines and cosines of $\alpha$ and $\beta$ . They can be derived from the unit circle or from $\cos(\alpha-\beta)$ ; in school you usually memorize the six main rows in the table below. The minus sign in the cosine of a sum is the classic pitfall: $\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta$ , while in the difference there is a plus before $\sin\alpha\sin\beta$ .

For $\tan$ always check the denominator $1\mp\tan\alpha\tan\beta\neq0$

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