Welcome to Trigonometry!
Trigonometric identities are equations involving trigonometric functions that are true for every value of the occurring variables where both sides of the equality are defined. These identities are useful tools for simplifying expressions and solving equations.
Fundamental Identities
- sin²(θ) + cos²(θ) = 1
- 1 + tan²(θ) = sec²(θ)
- 1 + cot²(θ) = csc²(θ)
Angle Sum and Difference Identities
- sin(α ± β) = sin(α)cos(β) ± cos(α)sin(β)
- cos(α ± β) = cos(α)cos(β) ∓ sin(α)sin(β)
- tan(α ± β) = (tan(α) ± tan(β)) / (1 ∓ tan(α)tan(β))
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