# Trigonometric Formulas

All classes equally use Trigonometric Formulas for their preparation. Practice these formulas by putting different values into them.

## Trigonometric Formulas

### Reciprocal Identities

• cosec θ = 1/sin θ
• sec θ = 1/cos θ
• cot θ = 1/tan θ
• sin θ = 1/cosec θ
• cos θ = 1/sec θ
• tan θ = 1/cot θ

### Inverse Trigonometry Formulas

• sin-1 (–α) = – sin-1 α
• cos-1 (–α) = π – cos-1 α = cos-1 α
• tan-1 (–α) = – tan-1 α
• cosec-1 (–α) = – cosec-1 α
• sec-1 (–α) = π – sec-1 α = sec-1 α
• cot-1 (–α) = π – cot-1 α = -cot-1α

### Cofunction Formulas

• sin(90° − α) = cos α
• cos(90° − α) = sin α
• tan(90° − α) = cot α
• cot(90° − α) = tan α
• sec(90° − α) = cosec α
• cosec(90° − α) = sec α

### Sum and Difference Formulas

• sin(α+β) = sinαcosβ + cosαsinβ
• sin(α-β) = sinαcosβ – cosαsinβ
• cos(α+β) = cosαcosβ – sinαsinβ
• cos(α-β) = cosαcosβ + sinαsinβ
• tan(α+β) = (tanα + tanβ) / (1 – tanαtanβ)
• tan(α+β) = (tanα – tanβ) / (1 + tanαtanβ)

### Half-Angle Formulas

sinα/2 = ±√(1-cosα)/2

cosα/2 = ±√(1+cosα)/2

tanα/2 = ±√(1-cosα)/(1+cosα)

### Double Angle Formulas

• sin2α = 2sinαcosα
• cos2α = cos2α – sin2α = 2cos2α – 1 = 1 – 2sin2α
• tan2α = 2tanα / (1 – tan2α)

### Triple Angle Formulas

• sin3α = 3sinα – 4sin3α
• cos3α = 4cos3α – 3cosα
• tan3α = 3tanα – tan3α / (1- 3tan2α)

### Product to Sum Formulas

• sinα + cosβ = 2 sin(α + β)/2 . cos (α – β)/2
• sinα – cosβ = 2 cos(α + β)/2 . sin (α – β)/2
• cosα + cosβ = 2 cos(α + β)/2 . cos (α – β)/2
• cosα – cosβ = -2 sin(α + β)/2 . sin (α – β)/2

### Sum to Product Formulas

• 2sinα . cosβ = sin(α + β) + sin(α – β)
• 2sinα . sinβ = cos(α – β) – cos(α + β)
• 2cosα . cosβ = cos(α + β) + cos(α – β)

#### By Ahsa.Pk

We are sharing meaningful and related notes and all materials for students.

#### 2nd Year Chemistry Important Short Questions

##### 2 thoughts on “Trigonometric Formulas”
1. Haziq says:

Please add chapter 12 and 13 formulae

1. They will also be added there in a short while.
Thanks for attention.

## You Missed

#### Austria Flag – Meaning and History

Don't Miss Out Anything!

Receive top education notes, lesson ideas, teaching tips, and more!

You have successfully subscribed to the newsletter

There was an error while trying to send your request. Please try again.

will use the information you provide on this form to be in touch with you and to provide updates and marketing.