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## Trigonometric Identities 21. $ \cos{A} - \cos{B} = -2\sin{\left(\frac{A+B}{2}\right)} \cdot \sin{\left(\frac{A-B}{2}\right)}$ 22. $\sin{2A} = 2 \sin{A} \cos{A}$ 23. $\cos{2A} = \cos^2{A} - \sin^2{A}$ 24. $\tan{2A} = \frac{2 \tan{A}}{1 - \tan^2{A}}$ 25. $\sin{3A} = 3 \sin{A} - 4 \sin^3{A}$ 2...

## Trigonometric Identities 21. $ \cos{A} - \cos{B} = -2\sin{\left(\frac{A+B}{2}\right)} \cdot \sin{\left(\frac{A-B}{2}\right)}$ 22. $\sin{2A} = 2 \sin{A} \cos{A}$ 23. $\cos{2A} = \cos^2{A} - \sin^2{A}$ 24. $\tan{2A} = \frac{2 \tan{A}}{1 - \tan^2{A}}$ 25. $\sin{3A} = 3 \sin{A} - 4 \sin^3{A}$ 26. $\cos{3A} = 4 \cos^3{A} - 3 \cos{A}$ 27. $\tan{3A} = \frac{3 \tan{A} - \tan^3{A}}{1 - 3 \tan^2{A}}$ 28. $\cos{(A+B)} - \cos{(A-B)} = -2 \sin{A} \sin{B}$ 29. $\cos{A} = \cos^2{\left(\frac{A}{2}\right)} - \sin^2{\left(\frac{A}{2}\right)}$ 30. $\tan{A} \pm \tan{B} = \frac{\sin{(A \pm B)}}{\cos{A} \cos{B}}$ 31. $\cot{A} + \cot{B} = \frac{\cos{(A+B)}}{\sin{A} \sin{B}}$ 32. $1 \pm \tan{A} \cdot \tan{B} = \frac{\cos{(A \pm B)}}{\cos{A} \cos{B}}$ 33. $\frac{1-\tan^2{A}}{1 + \tan^2{A}} = \cos{2A}$ 34. $2 \tan{A} = \frac{1 + \tan^2{A}}{1 + \tan^2{A}}$ 35. $1 \pm \sin{2A} = (\cos{A} \pm \sin{A})^2$ 36. $\sin{\theta} \sin{(60^\circ - \theta)} \sin{(60^\circ + \theta)} = \frac{1}{4} \sin{3 \theta}$ 37. $\cos{\theta} \cos{(60^\circ - \theta)} \cos{(60^\circ + \theta)} = \frac{1}{4} \cos{3 \theta}$ 38. $a \sin{\theta} + b \cos{\theta} = \sqrt{a^2 + b^2} \left( \sin{(\theta + \phi)}\right)$