trig identities

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27 Terms

1
sin(−𝜃) \=
− sin 𝜃
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2
cos(−𝜃) \=
cos 𝜃
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3
tan(−𝜃) \=
− tan 𝜃
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4
csc(−𝜃) \=
− csc 𝜃
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5
sec(−𝜃) \=
sec 𝜃
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6
cot(−𝜃) \=
− cot 𝜃
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7
tan 𝜃 \=
sin 𝜃/cos 𝜃
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8
cot 𝜃 \=
cos 𝜃/sin 𝜃
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9
sin^2 𝜃 + cos^2 𝜃 \=
1
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10
tan^2 𝜃 + 1 \=
sec^2 𝜃
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11
cot^2 𝜃 + 1 \=
csc^2 𝜃
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12
sin 2𝜃
\= 2 sin 𝜃cos 𝜃
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13
cos 2𝜃
\= cos^2 𝜃 − sin^2 𝜃
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14
cos 2𝜃
\= 2 cos^2 𝜃 − 1
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15
cos 2𝜃
\= 1 − 2 sin^2 𝜃
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16
tan 2𝜃
\= 2 tan 𝜃/1 − tan2
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17
sin(𝐴± 𝐵) \=
sin 𝐴 cos𝐵 ± cos 𝐴 sin 𝐵
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18
cos(𝐴± 𝐵) \=
cos𝐴 cos 𝐵 ∓ sin 𝐴 sin𝐵
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19
tan(𝐴 ± 𝐵) \=
(tan 𝐴 ± tan𝐵)/(1 ∓ tan𝐴 tanB)
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20
sin 𝐴 sin 𝐵 \=
1/2 [cos(𝐴 − 𝐵) − cos(𝐴 + 𝐵)]
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21
cos 𝐴 cos 𝐵 \=
1/2[cos(𝐴 + 𝐵) + cos(𝐴 − 𝐵)]
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22
sin 𝐴 cos 𝐵 \=
1/2 [sin(𝐴 + 𝐵) + sin(𝐴 − 𝐵)]
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23
cos 𝐴 sin 𝐵 \=
1/2 [sin(𝐴 + 𝐵) − sin(𝐴 − 𝐵)
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24
sin𝐴 + sin𝐵 \=
2 sin[(𝐴+𝐵)/2] cos [(𝐴−𝐵)/2]
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25
sin𝐴 − sin𝐵 \=
2 cos [(𝐴+𝐵)/2]sin[(𝐴−𝐵)/2]
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26
cos𝐴 + cos𝐵 \=
2 cos [(𝐴+𝐵)/2] cos [(𝐴−𝐵)/2]
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27
cos𝐴 − cos𝐵 \=
−2 sin [(𝐴+𝐵)/2]sin[(𝐴− 𝐵)/2]
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