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Sec, Cosec and Cot Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. sec x = 1 cos x cosec x = 1 sin x 1 = cos x tan x sin x cot x = Note, sec x is not the same as cos-1x (sometimes written as arccos x). Remember, you cannot divide by zero and so these definitions are only valid when the denominators are not zero. Example If sec x = 2, cos x = ½, x = 60º Graphs of sec x and cosec x Pythagorean Identities The identity: sin²x + cos²x = 1 can be used to derive two more important identities: By dividing each of these terms by sin²x, we can derive a second identity: • 1 + cot²x = cosec²x By dividing (*) by cos²x, we arrive at the third (and final) identity: • tan²x + 1 = sec²x These identities work for any angle x (measure in either degrees or radians).