Trigonometric Formulas

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

Trigonometric Formulas

Trigonometric Table

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)