Trigonometric Identities

There are various identities that can be proven regarding trigonmetric functions. In a right angled triangle $tan\theta=\frac{O}{A}$ , and since $cos\theta=\frac{A}{H}$ and $sin\theta=\frac{O}{H}$ :

$tan\theta\equiv\frac{sin\theta}{cos\theta}$

In a right angled triangle $H^2=O^2+A^2$ So: (Hcosθ)² + (Hsinθ)² = H² (cosθ)² + (sinθ)² = 1

$cos^2\theta+sin^2\theta\equiv1$