Trig Identities

Reciprocal Identities §

csc x = $\frac{1}{sinx}$ sec x = $\frac{1}{cosx}$ cot x = $\frac{1}{tanx}$

Quotient Identities §

$\frac{sinx}{cosx}$ = tan x $\frac{cosx}{sinx}$ = cot x

Reciprocal Identities §

Square both sides csc${}^2$ x = $\frac{1}{si{n}^{2}x}$ sec${}^2$ x = $\frac{1}{co{s}^{2}x}$ cot${}^2$ x = $\frac{1}{ta{n}^{2}x}$

Pythagorean Identities §

sin${}^2$x + cos${}^2$x = 1 Rearrange the identity sin${}^2$ x = 1 - cos${}^2$ x cos${}^2$ x = 1 - sin${}^2$ x

1 + cot${}^2$ x = csc${}^2$ x tan${}^2$ x + 1 = sec${}^2$ x

Co-Function Identities §

sin($\frac{\pi }{2}$ - x) = cos x csc($\frac{\pi }{2}$ - x) = sec x cos($\frac{\pi }{2}$ - x) = sin x sec($\frac{\pi }{2}$ - x) = csc x tan($\frac{\pi }{2}$ - x) = cot x cot($\frac{\pi }{2}$ - x) = tan x

Even-odd identities §

sin(-x) = - sin x csc(-x) = - csc x cos(-x) = cos x sec(-x) = sec x tan(-x) = - tan x cot(-x) = - cot x

Sum-Difference formulas §

sin(x $\pm$ y) = sin x cos y $\pm$ cos x sin y cos(x $\pm$ y) = cos x cos y $\mp$ sin x sin y tan(x $\pm$ y) = $\frac{tanx+/-tany}{1-/+tanxtany}$

Double Angle Formulas §

sin(2x) = 2 sin x cos x cos(2x) = cos${}^2$ x - sin ${}^2$ x = 2 cos${}^2$ x - 1 = 1 - 2sin${}^2$ x tan(2x) = $\frac{2tanx}{1-ta{n}^{2}x}$