Trigonometric Functions

Front: If A + B = 180°
Back: sin A = sin B, cos A + cos B = 0, tan A + tan B = 0

Front: If A + B = 90°
Back: sin A = cos B, cos A = sin B

Front: sin(A + B)
Back: sin A cos B + cos A sin B

Front: sin(A - B)
Back: sin A cos B - cos A sin B

Front: cos(A + B)
Back: cos A cos B - sin A sin B

Front: cos(A - B)
Back: cos A cos B + sin A sin B

Front: tan(A + B)
Back: (tan A + tan B) / (1 - tan A tan B)

Front: tan(A - B)
Back: (tan A - tan B) / (1 + tan A tan B)

Front: cot(A + B)
Back: (cot A cot B - 1) / (cot B + cot A)

Front: cot(A - B)
Back: (cot A cot B + 1) / (cot B - cot A)

Front: sin² A - sin² B
Back: sin(A + B) sin(A - B)

Front: cos² A - cos² B
Back: cos(A + B) cos(A - B)

Front: sin 2θ
Back: 2 sin θ cos θ = (2 tan θ) / (1 + tan² θ)

Front: cos 2θ
Back: 2 cos² θ - 1 = 1 - 2 sin² θ = (1 - tan² θ) / (1 + tan² θ)

Front: tan 2θ
Back: (2 tan θ) / (1 - tan² θ)

Front: sin 3θ
Back: 3 sin θ - 4 sin³ θ

Front: cos 3θ
Back: 4 cos³ θ - 3 cos θ

Front: tan 3θ
Back: (3 tan θ - tan³ θ) / (1 - 3 tan² θ)

Front: sin(A + B) + sin(A - B)
Back: 2 sin A cos B

Front: sin(A + B) - sin(A - B)
Back: 2 cos A sin B

Front: cos(A + B) + cos(A - B)
Back: 2 cos A cos B

Front: cos(A + B) - cos(A - B)
Back: -2 sin A sin B

Front: sin A + sin B
Back: 2 sin((A + B)/2) cos((A - B)/2)

Front: sin A - sin B
Back: 2 cos((A + B)/2) sin((A - B)/2)

Front: cos A + cos B
Back: 2 cos((A + B)/2) cos((A - B)/2)

Front: cos A - cos B
Back: -2 sin((A + B)/2) sin((A - B)/2)

Front: cos² θ
Back: (1 + cos 2θ) / 2

Front: sin² θ
Back: (1 - cos 2θ) / 2

Front: tan² θ
Back: (1 - cos 2θ) / (1 + cos 2θ)

Front: (cosθ + sinθ)²
Back: 1 + sin 2θ

Front: (cosθ - sinθ)²
Back: 1 - sin 2θ

Front: tan(π/4 + θ)
Back: (1 + tan θ) / (1 - tan θ)

Front: tan(π/4 - θ)
Back: (1 - tan θ) / (1 + tan θ)

Front: sin(A + B) sin(A - B)
Back: sin² A - sin² B

Front: cos(A + B) cos(A - B)
Back: cos² A - sin² B

Front: tan(A + B + C)
Back: (tan A + tan B + tan C - tan A tan B tan C) / (1 - tan A tan B - tan B tan C - tan C tan A)

Front: sinθ sin(60° - θ) sin(60° + θ)
Back: (1/4) sin 3θ°

Front: cosθ cos(60° - θ) cos(60° + θ)
Back: (1/4) cos 3θ°

Front: tanθ tan(60° - θ) tan(60° + θ)
Back: tan 3θ°