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1 Math 19 - Fall 2014 Trigonometry There are a few trigonometric identities which we must learn to identify on sight. The main point with memorizing these particular identities is a recognition question. For several types of calculus problems, it must occur to you at a certain point that one of these identities would simplify your work, or you simply cannot continue with the problem. Without them, you would simply stare at a blank page or waste your time doing something which cannot succeed. Pythagorean identities: sin2 x + cos2 x = 1 tan2 x + 1 = sec2 x 1 + cot2 x = csc2 x Double angle formulas for sin and cos sin 2x = 2 sin x cos x cos 2x = cos2 x − sin2 x Combining the double angle formula for cosine with the first Pythagorean identity, we get a “power lowering” formula for both sin and cos. This is vital for integrating the left side of each identity. sin2 x = cos2 x = 1−cos 2x 2 1+cos 2x 2 Addition formulas for sin, cos and tan 2 sin(x + y) = sin x cos y + cos x sin y cos(x + y) = cos x cos y − sin x sin y tan(x + y) = tan x+tan y 1−tan x tan y