1.

[latex]5 \tan 135° + 6 \cos 60°[/latex]

2.

[latex]3 \tan 240° + 8 \sin 300°[/latex]

3.

[latex]\sin (15° + 30°)[/latex]

4.

[latex]\cos(2 \cdot 75°)[/latex]

5.

[latex]8 \cos^2 (30°)[/latex]

6.

[latex]12 \sin^2 (315°)[/latex]

7.

[latex]3 \tan^2 (150°) - \sin^2 (45°)[/latex]

8.

[latex]1 + \tan^2 (120°)[/latex]

9.

[latex]3 \sin x + 5 \cos y[/latex]

10.

[latex]4 \tan y + 6 \cos y[/latex]

11.

[latex]-2 \tan 3y[/latex]

12.

[latex]\sin (3z - 2x)[/latex]

13.

[latex]\cos^2 x + \sin^2 x[/latex]

14.

[latex]7 \sin^2 y + 7 \cos^2 y[/latex]

15.

[latex]\cos x \cos x - \sin x \sin z[/latex]

16.

[latex]\tan (180° - x) \tan x[/latex]

17.

1. [latex]\sin (10° + 40°)[/latex]
2. [latex]\sin 10° + \sin 40°[/latex]
3. [latex]\sin 10° \cos 40° + \cos 10° \sin 40°[/latex]

18.

1. [latex]\cos (20° + 50°)[/latex]
2. [latex]\cos 20° + \cos 50°[/latex]
3. [latex]\cos 20° \cos 50° - \sin 20° \sin 50°[/latex]

19.

1. [latex]\cos (2 \cdot 24°)[/latex]
2. [latex]2 \cos 24°[/latex]
3. [latex]2 \cos^2 (24°) - 1[/latex]

20.

1. [latex]\cos (3 \cdot 49°)[/latex]
2. [latex]3 \cos 49°[/latex]
3. [latex]4 \cos^3 (49°) - 3\cos 49°[/latex]

21.

1. [latex]\cos^2 (17°) + \sin^2 (17°)[/latex]
2. [latex]\cos^2 (86°) + \sin^2 (86°)[/latex]
3. [latex]\cos^2 (111°) + \sin^2 (111°)[/latex]

22.

1. [latex]\dfrac{1}{\cos^2 (25°)} - \tan^2 (25°)[/latex]
2. [latex]\dfrac{1}{\cos^2 (100°)} - \tan^2 (100°)[/latex]
3. [latex]\dfrac{1}{\cos^2 (8°)} - \tan^2 (8°)[/latex]

23.

1. [latex]3x^2 - x - 5x^2[/latex]
2. [latex]3\cos^2 \theta - \cos \theta - 5\cos^2 \theta[/latex]

24.

1. [latex]4x + 5y - y[/latex]
2. [latex]4\cos \theta + 5\sin \theta - \sin \theta[/latex]

25.

1. [latex]-3SC + 7SC[/latex]
2. [latex]-3\sin \theta \cos \theta + 7\sin \theta \cos \theta[/latex]

26.

1. [latex]4SC + 11SC - 17SC[/latex]
2. [latex]4\sin \theta \cos \theta + 11\sin \theta \cos \theta - 17\sin \theta \cos \theta[/latex]

27.

1. [latex]-C^2S^3 + 6C^2S^3[/latex]
2. [latex]-\cos^2 \theta \sin^3 \theta + 6 \cos^2 \theta \sin^3 \theta[/latex]

28.

1. [latex]7C^2S^2 - (2CS)^2[/latex]
2. [latex]7\cos^2 \theta \sin^2 \theta - (2\cos \theta \sin \theta)^2[/latex]

29.

[latex]\cos t + 2 \cos t \sin t - 3 \cos t,[/latex] for [latex]t = 143°[/latex]

30.

[latex]11 \tan w - 4 \tan w + 6 \tan w \cos w,[/latex] for [latex]w = 8°[/latex]

31.

[latex]7 \tan \theta - 4 \tan \phi + 3 \tan \phi - 6 \tan \theta,[/latex] for [latex]\theta = 21 °, ~ \phi = 89°[/latex]

32.

[latex]5 \sin A + \sin B - 6\sin B + 6 \sin A,[/latex] for [latex]A = 111°,~ B = 26°[/latex]

33.

[latex]-\sin x \cos x - \sin (2x) + 3\sin x \cos x,[/latex] for [latex]x = 107°[/latex]

34.

[latex]4 \cos u \sin u + 3 \sin 2u - 10 \sin u \cos u,[/latex] for [latex]u = 2°[/latex]

35.

[latex]\cos (x + y),~~\cos x + \cos y[/latex]

36.

[latex]\sin (\theta - \phi),~~\sin \theta - \sin \phi[/latex]

37.

[latex]\tan (2A),~~ 2 \tan A[/latex]

38.

[latex]\cos (\frac{1}{2}\beta),~~\frac{1}{2}\cos \beta[/latex]

39.

[latex](\sin \alpha)^2,~~\sin^2 \alpha[/latex]

40.

[latex](\tan B)^2,~~ \tan (B^2)[/latex]

41.

[latex]\sin 3t + \sin 5t,~~\sin 8t[/latex]

42.

[latex]3\cos 2x + 5\cos 2x,~~ 8\cos 2x[/latex]

43.

[latex]\tan (\theta + 45°) - \tan \theta,~~ \tan 45°[/latex]

44.

[latex]\sin (30° + z) + \sin (30° - z),~~ \sin 60°[/latex]

45.

1. [latex]x(2x-1)[/latex]
2. [latex]\sin A (2\sin A - 1)[/latex]

46.

1. [latex]q(5r-q)[/latex]
2. [latex]\cos \theta (5\sin \theta - \cos \theta)[/latex]

47.

1. [latex]a(b - 3a)[/latex]
2. [latex]\tan A (\tan B - 3 \tan A)[/latex]

48.

1. [latex]3w(2w - z)[/latex]
2. [latex]3 \sin \alpha (2 \sin \alpha - \sin \beta)[/latex]

49.

1. [latex](C + 1)(2C - 1)[/latex]
2. [latex](\cos \phi + 1)(2\cos \phi - 1)[/latex]

50.

1. [latex](3S - 2)(S + 1)[/latex]
2. [latex](3\sin B - 2)(\sin B + 1)[/latex]

51.

1. [latex](a + b)(a - b)[/latex]
2. [latex](\cos \theta + \cos \phi)(\cos \theta - \cos \phi)[/latex]

52.

1. [latex](t - w)(t + 4w)[/latex]
2. [latex](\tan \alpha - \tan \beta)(\tan \alpha + 4 \tan \beta)[/latex]

53.

1. [latex](1 - T)^2[/latex]
2. [latex](1 - \tan \theta)^2[/latex]

54.

1. [latex](2 + 3S)^2[/latex]
2. [latex](2 + 3\sin \theta)^2[/latex]

55.

1. [latex](T^2 + 2)(T^2 - 2)[/latex]
2. [latex](\tan^2 \theta + 2)(\tan^2 \theta - 2)[/latex]

56.

1. [latex](2c^2 - 3)(2c^2 + 3)[/latex]
2. [latex](2\cos^2\phi - 3)(2\cos^2 \phi + 3)[/latex]

57.

1. [latex]9m + 15n[/latex]
2. [latex]9\cos\alpha + 15\cos\beta[/latex]

58.

1. [latex]12p - 20q[/latex]
2. [latex]12\sin \theta - 20 \sin \phi[/latex]

59.

1. [latex]5r^2 - 10 qr[/latex]
2. [latex]5\tan^2 C - 10 \tan B \tan C[/latex]

60.

1. [latex]2x^2 - 6xy[/latex]
2. [latex]2\sin^2 a - 6\sin A \cos A[/latex]

61.

1. [latex]9C^2 - 1[/latex]
2. [latex]9\cos^2 \beta - 1[/latex]

62.

1. [latex]25S^2 - 16S[/latex]
2. [latex]25\sin^2 \beta - 16 \sin \beta[/latex]

63.

1. [latex]6T^3 - 8T^2[/latex]
2. [latex]6\tan^3 A - 8 \tan^2 A[/latex]

64.

1. [latex]9T^2 - 15T^3[/latex]
2. [latex]9\tan^2 B - 15\tan^3 B[/latex]

65.

1. [latex]t^2 - t - 20[/latex]
2. [latex]\tan^2 \theta - \tan \theta - 20[/latex]

66.

1. [latex]s^2 + 5s - 6[/latex]
2. [latex]\sin^2 A + 5 \sin A - 6[/latex]

67.

1. [latex]3c^2 + 2c - 1[/latex]
2. [latex]3\cos^2 B + 2\cos B - 1[/latex]

68.

1. [latex]8S^2 - 6S + 1[/latex]
2. [latex]8\sin^2 \phi - 6 \sin \phi + 1[/latex]

69.

1. [latex]6S^2 - 5S - 1[/latex]
2. [latex]6\sin^2 \alpha - 5\sin \alpha - 1[/latex]

70.

1. [latex]T^2 - 4T - 12[/latex]
2. [latex]\tan^2 \alpha - 4\tan \alpha - 12[/latex]