Trig Identites

1/csc(x)

sin (x)

1/sec(x)

cos(x)

1/cot(x)

tan(x)

sin²θ + cos²θ

1

1 + tan²(x)

sec²(x)

1 + cot²(x)

csc²(x)

sin(π/2−x)

cos(x)

cos(π/2−x)

sin(x)

tan(π/2 - x)

cot(x)

cot(π/2 - x)

tan(x)

sec(π/2 - x)

csc(x)

csc(π/2 - x)

sec(x)

±√(1 - cos(x)/2

sin(x/2)

±√(1 + cos(x)/2

cos(x/2)

±√(1 - cos(x)/1+cos(x)

tan(x)/2

2sin(x)cos(x)

sin(2x)

2tan(x)/(1-tan²(x))

tan(2x)

1-2sin²x

cos(2x)

2cos²x-1

cos(2x)

cos²x-sin²x

cos(2x)

sin(-x)

-sin(x)

csc(-x)

-csc(x)

cos(-x)

cos(x)

sec(-x)

sec(x)

tan(-x)

-tan(x)

cot(-x)

-cot(x)

1/sin(x)

csc(x)

1/cos(x)

sec(x)

1/tan(x)

cot(x)

sin(x)/cos(x)

tan(x)

cos(x)/sin(x)

cot(x)

sin(a)cos(b)+cos(a)sin(b)

sin(a+b)

sin(a)cos(b)−cos(a)sin(b)

sin(a−b)

cos(a)cos(b)−sin(a)sin(b)

cos(a+b)

cos(a)cos(b)+sin(a)sin(b)

cos(a−b)

tan(a)+tan(b)/1-tan(a)tan(b)

tan(a+b)

tan(a)-tan(b)/1+tan(a)tan(b)

tan(a−b)