1. Trigonometry Formulas of the six trigonometric ratios:
1. Sinθ = Opposite side/Hypotenuse
2. Cosθ = Adjacent side/Hypotenuse
3. Tanθ = Opposite side/Adjacent side
4. Cosec θ = Hypotenuse/Opposite side
5. Sec θ = Hypotenuse/Adjacent side
6. Cot θ = Adjacent side/ Opposite side
2. Tanθ = Sinθ/Cosθ.
Cosec = 1/Sinθ.
Secθ = 1/ Cosθ.
Cotθ = 1/ tanθ. Also, Cotθ = Cosθ /Sinθ
3. Trigonometric Formulas on trigonometric identities
1. sin 2θ + cos2θ = 1.
So, sin2θ = 1 – cos2θ, and cos2θ = 1 – sin2θ
2. cosec2θ – cot2θ = 1.
So, cosec2θ = 1 + cot2θ, and cosec2θ – 1 = cot2θ.
3. sec2θ – tan2θ = 1.
So, sec2θ = 1 + tan2θ, and sec2θ – 1 = tan2θ
4. Trigonometric Formulas on compound angles:
1. sin (A + B) = sinAcosB + cosAsinB
2. sin (A – B) = sinAcosB – cosAsinB
3. cos(A + B) = cosAsinB – sinAcosB
4. cos(A – B) = cosAsinB + sinAcosB
5. tan (A + B) = tan A + tan B/(1 – tanAtanB)
6. tan (A – B) = tan A – tan B/(1 + tanAtanB)
7. sin (A + B) sin (A – B) = sin 2 A – sin 2 B
8. cos(A + B) cos(A – B) = cos 2 A – sin 2 B
5. Trigonometric Formulas on Multiple Angles
1. Sin2A = 2sinAcosA.
Also, Sin2A = 2tanA/ (1 + tan2 A)
2. Cos2A = cos2A – sin2A
Also, Cos2A = (1 – tan2A)/(1 + tan2A), and
Cos2A = 2cos2A – 1, and
Cos2A = 1 – 2sin2A
3. Sin 3A = 3sinA – 4sin3A
4. Cos3A = 4cos3A – 3cosA
5. Tan 3A = (3tanA – tan3A)/(1 – 3tan3A)