# 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)

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