Basic Trigonometry Proofs

Mathematical identities relates one mathematical expression to another. Similarly, trigonometry identities relates one trigonometric expression to another, different, trigonometric expression. Trigonometry identities aids us in simplifying complex trigonometric functions, expressions and formulas. This used everywhere in the practical world. These identities are required to be learned at school.

Mathematical proofs is a substantiated argument that logically explains statements or assumptions made. Similarly, trigonometric proofs is a substantiated argument that logically explains trigonometric statements or assumptions made. The proofs of these trigonometric identities are frequently part of school curriculums.

Do these trigonometric expressions make logical sense? How does one prove it? Or did someone simply made them up?

This course contains detailed proofs of the following trigonometric identities:

• Area ΔABC = 0.5⋅b⋅c⋅sin(A)

• sinθ = cos(90° - θ)

• cosθ = sin(90° - θ)

• tanθ = sinθ / cosθ

• (sinθ)^2 + (cosθ)^2 = 1

• sin(x+y) = sinx⋅cosy + cosx⋅siny

• sin(x-y) = sinx⋅cosy - cosx⋅siny

• cos(x+y) = cosx⋅cosy - sinx⋅siny

• cos(x-y) = cosx⋅cosy + sinx⋅siny

• sin(2θ) = 2sinθ⋅cosθ

• cos(2θ) = (cosθ)^2 -(sinθ)^2

By understanding where these trigonometric identities come from, by proving them, we can gain a better and deeper understanding of these identities. This equips us to apply these identities with a deep understanding of its uses and where it comes from.

This course thoroughly explains these trigonometric identities and proves them, step by step. This is done by making use of basic trigonometric rules and mathematical concepts. It equips students to understand them better and use them better.