Trig identities
sin²x + cos²x = 1. tan x = sin x / cos x. Reciprocal: cosec, sec, cot.
Memorise: sin² + cos² = 1, tan = sin/cos, 1 + tan² = sec², 1 + cot² = cosec². Reciprocal definitions: cosec = 1/sin, sec = 1/cos, cot = 1/tan.
Worked examples
sin² x = 1 − cos² x.
tan x × cos x = sin x.
(sin x + cos x)² = 1 + 2 sin x cos x = 1 + sin 2x.
Frequently asked questions
How to remember 1 + tan² = sec²?
Divide sin² + cos² = 1 by cos²: tan² + 1 = sec².
Cot is just 1/tan?
Yes; also cos/sin.