Trig Identities

sin²x + cos²x

1

1+tan²x

sec²x

1+cot²x

cosec²x

sin(−x)

−sin x

cos (-x)

cos x

tan (-x)

-tanx

sin(x+2π)

sinx

cos(x+2π)

cos x

tan(x+π)

tan x

sin(90−x)

cos x

cos(90−x)

sin x

tan(90−x)

cot x

sin(180−x)

sin x

cos(180−x)

−cos x

tan(180−x)

−tan x

sin(180+x)

−sin x

cos(180+x)

−cos x

tan(180+x)

tan x

sin (A±B)

sin A . cos B ± cos A . sin B

cos (A±B)

cos A . cos B∓ sin A . sin B

tan(A±B)

(1 ∓ tan A tan B) / (tan A ± tan B​)

sin2x

2sinxcosx

cos2x

cos²x−sin²x

1−2sin²x

2cos²x−1

tan 2x

2tanx / (1−tan²x​)

sin3x

3sinx−4sin³x

cos3x

4cos³x−3cosx

tan 3x

(3tanx - tan³x) / (1-3tan²x)

tan(x/2)

​(1−cosx​) / sin x

sin x / (1+cosx)

2 sin A sin B

cos(A−B)−cos(A+B)

2cos A cos B

cos(A−B)+cos(A+B)

2sin A cos B

sin(A+B)+sin(A−B)

sin x + cos x

2^1/2sin (x + 45)

sin x - cos x

2^1/2sin (45 - x)

a sin x + b cos x

(a² + b² )^1/2 sin [x+tan^-1(b/a)]

∣ sin x + cos x ∣ ≤

2^1/2

sin x + cos x = 2^1/2 when x = ?

45 + 2n(pi)

sin x = sin2x

2x=x+2nπ

OR

2x=π−x+2nπ

lim_x→0(sin/x)

1

sin x ≈

x - x³/6

cos x ≈

1 - x²/2

sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C IF??

A + B + C = Pi

sin (a + b) sin (a - b)

sin²a - sin²b