Notes@HKU by Jax

Trigonometry review

Trigonometric identities

  1. sin⁡2x+cos⁡2x=1\sin^2x+\cos^2x=1
  2. tan⁡x=sin⁡xcos⁡x\tan x=\frac{\sin x}{\cos x}
  3. csc⁡x=1sin⁡x\csc x=\frac{1}{\sin x}
  4. sec⁡x=1cos⁡x\sec x=\frac{1}{\cos x}
  5. cot⁡x=1tan⁡x\cot x=\frac{1}{\tan x}
  6. sin⁡2x=2sin⁡xcos⁡x\sin 2x=2\sin x\cos x
  7. cos⁡2x=cos⁡2x−sin⁡2x\cos 2x=\cos^2x-\sin^2x
  8. tan⁡2x=2tan⁡x1−tan⁡2x\tan 2x=\frac{2\tan x}{1-\tan^2x}
  9. sin⁡(x±y)=sin⁡xcos⁡y±cos⁡xsin⁡y\sin(x\pm y)=\sin x\cos y\pm\cos x\sin y
  10. cos⁡(x±y)=cos⁡xcos⁡y∓sin⁡xsin⁡y\cos(x\pm y)=\cos x\cos y\mp\sin x\sin y
  11. tan⁡(x±y)=tan⁡x±tan⁡y1∓tan⁡xtan⁡y\tan(x\pm y)=\frac{\tan x\pm\tan y}{1\mp\tan x\tan y}
  12. 1+tan2x=sec2x1 + tan^2x = sec^2x
  13. 1+cot2x=csc2x1 + cot^2x = csc^2x

Related: Techniques of integration

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