Download sin x + cos 2 x = 1 tan2 x + 1 = sec 1 + cot2 x = csc sin 2x = 2

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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