Pythagorean identity sin^2α + cos^2α = 1. tanα = sinα / cosα, ctgα = cosα / sinα. Product of tan and cot the same able equals 1: tanα * cotα = 1. sin(90° - α) = cosα, cos(90° - α) = sinα, tan(90° - α) = cotα, cot(90° - α) = tanα, sin(180° - α) = sinα, cos(180° - α) = -cosα, tan(180° - α) = -tanα, cot(180° - α) = -cotα.