Trig identities

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Last updated 8:48 AM on 5/12/26
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12 Terms

1
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sin⁡2x+cos⁡2x=\sin^2x+\cos^2x=

1

2
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1+tan⁡2x=1+\tan^2x=

sec2xsec^2x

3
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1+cot⁡2x=1+\cot^2x=

csc⁡2x\csc^2x

4
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sin⁡(90−x)=\sin\left(90-x\right)=

cos⁡x\cos x

5
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tan⁡(90−x)=\tan\left(90-x\right)=

cotxcotx

6
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sec⁡(90−x)=\sec\left(90-x\right)=

cscxcscx

7
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sin⁡(A−B)=\sin\left(A-B\right)=

(sin⁡A)(cos⁡B)+(cos⁡A)(sin⁡B)\left(\sin A\right)\left(\cos B\right)+\left(\cos A\right)\left(\sin B\right)

8
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sin⁡(A−B)=\sin\left(A-B\right)=

(sin⁡A)(cos⁡B)−(cos⁡A)(sin⁡B)\left(\sin A\right)\left(\cos B\right)-\left(\cos A\right)\left(\sin B\right)

9
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cos⁡(A+B)=\cos\left(A+B\right)=

(cos⁡A)(cos⁡B)−(sin⁡A)(sin⁡B)\left(\cos A\right)\left(\cos B\right)-\left(\sin A\right)\left(\sin B\right)

10
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cos⁡(A−B)=\cos\left(A-B\right)=

(cos⁡A)(cos⁡B)+(sin⁡A)(sin⁡B)\left(\cos A\right)\left(\cos B\right)+\left(\sin A\right)\left(\sin B\right)

11
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tan⁡(A+B)=\tan\left(A+B\right)=

tan⁡A+tan⁡B1−(tan⁡A)(tan⁡B)\frac{\tan A+\tan B}{1-\left(\tan A\right)\left(\tan B\right)}

12
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tan⁡(A−B)=\tan\left(A-B\right)=

tan⁡A−tan⁡B1+(tan⁡A)(tan⁡B)\frac{\tan A-\tan B}{1+\left(\tan A\right)\left(\tan B\right)}