Quick Recap — Compound & Multiple Angles

  • sin⁡(A±B)=sin⁡Acos⁡B±cos⁡Asin⁡B\sin(A\pm B)=\sin A\cos B\pm\cos A\sin B; cos⁡(A±B)=cos⁡Acos⁡B∓sin⁡Asin⁡B\cos(A\pm B)=\cos A\cos B\mp\sin A\sin B.
  • tan⁡(A+B)=tan⁡A+tan⁡B1−tan⁡Atan⁡B\tan(A+B)=\dfrac{\tan A+\tan B}{1-\tan A\tan B}.
  • sin⁡2A=2sin⁡Acos⁡A\sin2A=2\sin A\cos A; cos⁡2A=cos⁡2A−sin⁡2A=1−2sin⁡2A=2cos⁡2A−1\cos2A=\cos^2A-\sin^2A=1-2\sin^2A=2\cos^2A-1; tan⁡2A=2tan⁡A1−tan⁡2A\tan2A=\dfrac{2\tan A}{1-\tan^2A}.
  • sin⁡3A=3sin⁡A−4sin⁡3A\sin3A=3\sin A-4\sin^3A; cos⁡3A=4cos⁡3A−3cos⁡A\cos3A=4\cos^3A-3\cos A.