# AP Precalculus Trig Identities

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sin²θ + cos²θ

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## Description and Tags

### 23 Terms

1

sin²θ + cos²θ

1

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2

1 + tan²θ

sec²θ

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3

1 + cot²θ

csc²θ

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4

sin(-u), csc(-u)

-sin(u), -csc(u)

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5

cos(-u), sec(-u)

cos(u), sec(u)

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6

tan(-u), cot(-u)

-tan(u), -cot(u)

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7

π/2 - θ relationships

sin-cos, csc-sec, tan-cot

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8

sin(u+v)

sinucosv + cosusinv

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9

sin(u-v)

sinucosv - cosusinv

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10

cos(u+v)

cosucosv - sinusinv

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11

cos(u-v)

cosucosv + sinusinv

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12

tan(u+v)

(tanu + tanv) / (1 - tanutanv)

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13

tan(u-v)

(tanu - tanv) / (1 + tanutanv)

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14

sin2θ

2sinθcosθ

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15

cos2θ

cos²θ-sin²θ

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16

cos2θ

2cos²θ-1

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17

cos2θ

1-2sin²θ

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18

tan2θ

(2tanθ)/(1 - tan²θ)

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19

sin(θ/2)

±sqrt((1-cosθ)/2))

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20

cos(θ/2)

±sqrt((1+cosθ)/2))

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21

tan(θ/2)

±sqrt((1-cosθ)/(1+cosθ))

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22

tan(θ/2)

((1-cosθ)/sinθ)

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23

tan(θ/2)

(sinθ)/(1+cosθ))

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