$$sec^2a= tan^2a+1$$

$$csc^2a= cot^2a+1$$

$$\int lnx dx=xlnx-x+C$$

$$\int tanx dx=-ln|cos x|+C$$

$$\int secx dx=ln |sec x +tan x|+C$$

$$\int cscx dx=ln |csc x -cot x|+C$$

$$\int \frac{dx}{a^2+x^2}=\frac{1}{a}\arctan(\frac{x}{a})+C$$

$$\int \frac{dx}{a^2-x^2}=\frac{1}{2a}\ln|\frac{a+x}{a-x}|+C$$

$$\int \frac{dx}{\sqrt{a^2-x^2}}=arcsin\frac{x}{a}+C$$

$$\int \frac{dx}{\sqrt{x^2\pm a^2}}=\ln|x+\sqrt{x^2\pm a^2}|+C$$

$$\int sec^2xdx=tanx+C$$

$$\int csc^2xdx=-cotx+C$$

$$\int secxtanxdx=secx+C$$

$$\int cscxcotxdx=-cscx+C$$

$$\int a^xdx=\frac{a^x}{lna}+C$$

$$\int e^xdx=e^x+C$$

$$sina cosb = \frac{1}{2}[sin(a+b)+sin(a-b)]$$

$$cosa sinb = \frac{1}{2}[sin(a+b)-sin(a-b)]$$

$$cosa cosb = \frac{1}{2}[cos(a+b)+cos(a-b)]$$

$$sina sinb = -\frac{1}{2}[cos(a+b)-cos(a-b)]$$

$$sin(a\pm b) = sinacosb\pm cosasinb$$

$$cos(a\pm b) = cosacosb-+sinasinb$$

$$sin x = \frac{2t}{1-t^2}$$

$$cos x = \frac{1-t^2}{1+t^2}$$

$$tan x = \frac{2t}{1-t^2}$$

$$dx = \frac{2}{1+t^2}dt$$