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Trigonometry

Those fundamental trigonometric identities are related with the properties of trigonometric functions. Some trigonometric identities or formulas are derived as mathematical equalities that are always true for used with trigonometric functions simlificaton and transformation .

The Double Angle Identities

For the angles sum identities, if the angles α and β are equal, then the angles sum identities can be reduced to double angle by letting θ=α=β. Imply

The Power Reduction Formulas

The double angle Identities for cosine function with power of sine and cosine functions can be used to reduce the power of sine and cosine functions through rearrangement of the equation. Imply

The Half Angle Identities

The power reduction formulas can be further elaborated to derive the half angle identities by substituting θ with θ/2. Imply

The Triple Angle Formulas

The triple angle formulas can be derived from the angles sum identities along with the double angle identities. Imply

The Product to Sum Formulas

The product to sum formulas can be derived directly from the angles sum and difference identities by making use of the addition and subtraction operations. Imply

The Sum to Product Formulas

By substitution, the product to sum formulas can be transformed to the sum to product formulas directly. Imply