If you are beginning to study freshmen calculus, it would be definitely a good idea to review some of the important formulas from precalculus before you get into more serious stuff in calculus. My top recommendation of such formulas would be the following.

Expansion of Polynomials

1. \((a+b)^2=a^2+2ab+b^2\)
2. \((a-b)^2=a^2-2ab+b^2\)
3. \((a+b)^3=a^3+3a^2b+3ab^2+b^3\)
4. \((a-b)^3=a^3-3a^2b+3ab^2-b^3\)

Factorization of Polynomials

1. \(a^2-b^2=(a+b)(a-b)\)
2. \(a^3-b^3=(a-b)(a^2+ab+b^2)\)
3. \(a^3+b^3=(a+b)(a^2-ab+b^2)\)

Trigonometric Identities

1. \(\cos^2\theta+\sin^2\theta=1\)
2. \(\tan^2\theta+1=\sec^2\theta\)

Sine Sum and Difference Formulas

1. \(\sin(\theta_1+\theta_2)=\sin\theta_1\cos\theta_2+\cos\theta_1\sin\theta_2\)
2. \(\sin(\theta_1-\theta_2)=\sin\theta_1\cos\theta_2-\cos\theta_1\sin\theta_2\)

Sine Double Angle Formula \[\sin2\theta=2\sin\theta\cos\theta\]

Cosine Sum and Difference Formulas

1. \(\cos(\theta_1+\theta_2)=\cos\theta_1\cos\theta_2-\sin\theta_1\sin\theta_2\)
2. \(\cos(\theta_1-\theta_2)=\cos\theta_1\cos\theta_2+\sin\theta_1\sin\theta_2\)

Cosine Double Angle Formula \begin{eqnarray*}\cos2\theta&=&\cos^2\theta-\sin^2\theta\\&=&2\cos^2\theta-1\\&=&1-2\sin^2\theta\end{eqnarray*}

From this Cosine Double Angle Formula, we obtain Half Angle Formulas.

Half Angle Formulas

1. \(\cos^2\theta=\displaystyle\frac{1+\cos2\theta}{2}\) or equivalently \(\cos\theta=\pm\sqrt{\displaystyle\frac{1+\cos2\theta}{2}}\)
2. \(\sin^2\theta=\displaystyle\frac{1-\cos2\theta}{2}\) or equivalently \(\sin\theta=\pm\sqrt{\displaystyle\frac{1-\cos2\theta}{2}}\)

For the above formulas from trigonometry, there are actually only three formulas you need to remember. They are $\cos^2\theta+\sin^2\theta=1$ and sine and cosine sum formulas. The rest of the formulas from trigonometry that are listed above can be stemmed from these three formulas.