Trigonometry formulas, identities, and calculus uses full!!! Every single one

sin x = opposite / hypotenuse

csc x = 1 / sin x

cos x = adjacent / hypotenuse

sec x = 1 / cos x

tan x = opposite / adjacent

cot x = 1 / tan x

sin x = 1 / csc x

csc x = 1 / sin x

cos x = 1 / sec x

sec x = 1 / cos x

tan x = 1 / cot x

cot x = 1 / tan x

tan x = sin x / cos x

cot x = cos x / sin x

sin²x + cos²x = 1

1

1 + tan²x = sec²x

sec²x − tan²x = 1

1 + cot²x = csc²x

csc²x − cot²x = 1

sin(−x) = −sin x

cos(−x) = cos x

tan(−x) = −tan x

sec(−x) = sec x

csc(−x) = −csc x

cot(−x) = −cot 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

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)

(tan a ± tan b) / (1 ∓ tan a tan b)

sin(2x)

2 sin x cos x

cos(2x)

cos²x − sin²x

cos(2x)

2cos²x − 1

cos(2x)

1 − 2sin²x

tan(2x)

(2 tan x) / (1 − tan²x)

sin²x

(1 − cos(2x)) / 2

cos²x

(1 + cos(2x)) / 2

sin(x/2)

±√[(1 − cos x)/2]

cos(x/2)

±√[(1 + cos x)/2]

tan(x/2)

sin x / (1 + cos x)

sin A sin B

1/2 [cos(A − B) − cos(A + B)]

cos A cos B

1/2 [cos(A − B) + cos(A + B)]

sin A cos B

1/2 [sin(A + B) + sin(A − B)]

sin A + sin B

2 sin((A + B)/2) cos((A − B)/2)

sin A − sin B

2 cos((A + B)/2) sin((A − B)/2)

cos A + cos B

2 cos((A + B)/2) cos((A − B)/2)

cos A − cos B

−2 sin((A + B)/2) sin((A − B)/2)

sin x cos x

(1/2) sin(2x)

d/dx (sin x)

cos x

d/dx (cos x)

−sin x

d/dx (tan x)

sec²x

d/dx (cot x)

−csc²x

d/dx (sec x)

sec x tan x

d/dx (csc x)

−csc x cot x

∫ sin x dx

−cos x + C

∫ cos x dx

sin x + C

∫ sec²x dx

tan x + C

∫ csc²x dx

−cot x + C

∫ sec x tan x dx

sec x + C

∫ csc x cot x dx

−csc x + C

d/dx (arcsin x)

1 / √(1 − x²)

d/dx (arccos x)

−1 / √(1 − x²)

d/dx (arctan x)

1 / (1 + x²)

d/dx (arcsec x)

1 / (|x|√(x² − 1))

d/dx (arccsc x)

−1 / (|x|√(x² − 1))

d/dx (arccot x)

−1 / (1 + x²)

√(a² − x²)

x = a sinθ

√(a² + x²)

x = a tanθ

√(x² − a²)

x = a secθ

t = tan(x/2)

sin x = 2t / (1 + t²)

t = tan(x/2)

cos x = (1 − t²) / (1 + t²)

t = tan(x/2)

tan x = 2t / (1 − t²)