trig formulas

sin (s+t)

\sin s\cos t+\sin t\cos s

sin (s-t)

\sin s\cos t-\sin t\cos s

cos (s+t)

\cos s\cos t-\sin s\sin t

cos (s-t)

\cos s\cos t+\sin s\sin t

tan (s+t)

\frac{\tan s+\tan t}{1-\tan s\tan t}

tan (s-t)

\frac{\tan s-\tan t}{1+\tan s\tan t}

sin (2x)

2\sin x\cos x

cos(2x)

\cos^2x-\sin^2x

1-2^{}\sin^2x 

2\cos^2x-1

tan (2x)

\frac{2\tan x}{1-\tan^2x}

\sin\frac{u}{2}

\frac{+}{}\sqrt{\frac{1-\cos u}{2}}

\cos\frac{u}{2}

\frac{+}{-}\sqrt{\frac{1+\cos u}{2}}

\tan\frac{u}{2}

\frac{1-\cos u}{\sin u}

\frac{\sin u}{1+\cos u}

\sin^2x

\frac{1-\cos\left(2x\right)}{2}

\cos^2x

\frac{1+\cos\left(2x\right)}{2}

sinAsinB

\frac12\left\lbrack\cos\left(A-B\right)-\cos\left(A+B\right)\right\rbrack

sinAcosB

\frac12\left\lbrack\sin\left(A-B\right)+\sin\left(A+B\right)\right\rbrack

cos A sin B

cosAcosB

\frac12\left\lbrack\cos\left(A-B\right)+\cos\left(A+B\right)\right\rbrack

sina + sinb

2\sin\frac{a+b}{2}\cos\frac{a-b}{2}

sina - sinb

2\cos\frac{a+b}{2}\sin\frac{a-b}{2}

cosa + cosb

2\cos\frac{a+b}{2}\cos\frac{a-b}{2}

cosa - cosb

-2\sin\frac{a+b}{2}\sin\frac{a-b}{2}

y=\sin^{-1}x

domain: [-1,1]

\left\lbrack-\frac{\pi}{2},\frac{\pi}{2}\right\rbrack range

quadrants 1 and 4

y=\cos^{-1}x

domain: [-1,1]

\left\lbrack0,\pi\right\rbrack range

quadrants 1 and 2

y=\tan^{-1}x

domain: all real numbers

\left(-\frac{\pi}{2},\frac{\pi}{2}\right) range

quadrants 1 and 4 (open circle at y-axis, closed at x-axis)