Math1014 Final Exam Formula Sheet Trigonometric Identities cos2 θ

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Math1014 Final Exam Formula Sheet
Trigonometric Identities
cos2 θ + sin2 θ = 1
sin(A + B) = sin A cos B + sin B cos A
1 + tan2 θ = sec2 θ
sin(A − B) = sin A cos B − sin B cos A
1 + cot2 θ = csc2 θ
cos(A + B) = cos A cos B − sin A sin B
sin 2θ = 2 sin θ cos θ
cos 2θ = 2 cos2 θ − 1 = 1 − 2 sin2 θ
tan 2θ =
2 tan θ
1 − tan2 θ
cos(A − B) = cos A cos B + sin A sin B
sin A cos B = 12 sin(A + B) + sin(A − B)
cos A cos B = 12 cos(A + B) + cos(A − B)
sin A sin B = 12 cos(A − B) − cos(A + B)
tan A + tan B
1 − tan A tan B
tan A − tan B
tan(A − B) =
1 + tan A tan B
tan(A + B) =
Z
Z
1
n−1
cos xdx = cosn−1 x sin x +
n
n
Z
1
n−1
sin xdx = − sinn−1 x cos x +
n
n
n
n
Z
Z
1
n−2
sec xdx =
secn−2 x tan x +
n−1
n−1
n
cosn−2 xdx
sinn−2 xdx
Z
secn−2 xdx
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