Trigonometry Formulas

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)