Basic formula: 

sin²(x) + cos²(x) = 1

Formulas that stem from it: 

1. sin²(x) = 1 - cos²(x) 

2. cos²(x) = 1 - sin²(x)

Basic formula: 

sin(2x) = 2sin(x)cos(x)

Formulas that stem from it: 

1. sin(2x) / 2 = sinx + cosx

Basic formula: 

cos(2x) = cos²(x) - sin²(x)

Formulas that stem from it: 

1. cos(2x) = 2cos²(x) - 1 or 1 = 2cos²(x) - cos(2x)

(this technically comes from the formula directly above)

2. cos²(x) = (cos(2x) +1) / 2 

3. cos(2x) = 1 - 2sin²(x)

Basic formula: 

1 = sec²(x) – tan²(x)

Formulas that stem from it: 

1. sec²(x) = 1 + tan²(x)

1. tan²(x) = sec²(x) - 1

Basic formula: 

cos(A + B) 

and

cos(A - B)

Formulas that stem from it: 

1. cos(A + B) = cosAcosB - sinAsinB

2. cos(A - B) = cosAsinB + cosBsinA

Basic formula: 

sin(A + B) 

and

sin(A - B)

Formulas that stem from it: 

1. sin(A + B) = sinAcosB + sinBcosA

2. sin(A - B) = sinAsinB - cosAcosB

Basic formulas for trigonometric functions and their steps

"(θ + 2π) & (θ + π)"

Formulas: 

1. sin(θ + 2π) = sinθ

2. cos(θ + 2π) = cosθ

3. tan(θ + π) = tanθ

Basic formula: 

tanθ = sinθ / cosθ

Formulas that stem from it: 

1. cotθ = cosθ/sinθ

(because cotangent is the inverse of tangent)

More trigonometric functions and their steps

Formulas: 

1. sin(π - θ) = sinθ

2. cos(π - θ) = -cosθ

3. tan(π - θ) = -tanθ

Some trigonometric formulas with a "3" inside the trig. function

Formulas: 

1. sin(3θ) = 3sinθ - 4sin³θ

2. cos(3θ) = 4cos³θ - 3cosθ

3. tan(3θ) = 3tanθ - tan³θ / (1 - 3tan²θ)

Finding all the trigonometric functions with only tangent !!

Formulas: 

1. sinθ = 2tan(θ/2) / (1 + tan²(θ/2))

2. cosθ = 1 - tan²(θ/2) / (1 + tan²(θ/2))

3. tanθ = 2tan(θ/2) / (1 - tan²(θ/2))

Odd and even trigonometric functions

Functions: 

1. sin(-x) = -sin(x)

2. cos(-x) = cos(x)

3. tan(-x) = -tan(x)