Trigonometric Identities

1/sin(x)

csc(x)

1/cos(x)

sec(x)

1/tan(x)

cot(x)

1/csc(x)

sin(x)

1/sec(x)

cos(x)

1/cot(x)

tan(x)

sin(x)/cos(x)

tan(x)

cos(x)/sin(x)

cot(x)

sin^2(x)+cos^2(x)

1 (a.k.a Big Papa)

sin^2(x)

1 - cos^2(x)

cos^2(x)

1 - sin^2(x)

tan^2(x)+1

sec^2(x)

tan^2(x)

sec^2(x)-1

sec^2(x) - tan^2(x)

1

1+cot^2(x)

csc^2(x)

cot^2(x)

csc^2(x) - 1

csc^2(x) - cot^2(x)

1

sin(A+B)

sin(A)cos(B) + cos(A)sin(B)

sin(A-B)

sin(A)cos(B) - cos(A)sin(B)

cos(A-B)

cos(A)cos(B) + sin(A)sin(B)

cos(A+B)

cos(A)cos(B) - sin(A)sin(B)

tan(A+B)

(tan(A)+tan(B))/(1-tan(A)tan(B))

tan(A-B)

(tan(A)-tan(B))/(1+tan(A)tan(B))

sin(2x)

2sin(x)cos(x)

cos(2x)

cos^2(x)-sin^2(x)

tan(2x)

2tan(x)/1-tan^2(x) -or- sin(2x)/cos(2x)

cos(2x) (Give Both Variations)

1 - 2sin^2(x) & 2cos^2(x)-1

sin(x/2)

sqrt((1 - cos(x)/2)

cos(x/2)

sqrt((1 + cos(x)/2)

tan(x/2)

Give both equations in terms of sine and cosine

(1 - cos(x))/sin(x) & sin(x)/(1 + cos(x))

• $\cos(2\theta) = 1 - 2\sin^2(\theta)$