Basic trigonometric identities can be algebraically manipulated to yield hundreds of other trigonometric identities. All trigonometric identities are based on these few fundamental ones. So, if you know these basic trigonometric identities by heart, then you know all other trigonometric identities (except those for compound and multiple angles, and those for negative angles):

Reciprocal relations between trigonometric ratios

Quotient relations between sine, cosine, tangent and cotangent ratios

Trigonometric identities between two - two trigonometric ratios

Reciprocal relations between trigonometric ratios

Trigonometric identities between two - two trigonometric ratios