The results of the trigonometric equations are listed below:
Herein we find ten trigonometric expressions whose values have to be found by using trigonometric formulas and definitions and the Pythagorean theorem. Now we proceed to solve for each case:
Case 1
cos 20° · cos 45° + sin 20° · sin 45°
cos 45° · cos 20° + sin 45° · sin 20°
cos (45° - 20°)
cos 25°
0.906
Case 2
cos 52° · cos 32° - sin 52° · sin 32°
cos (52° - 32°)
cos 20°
0.940
Case 3
sin 22° · cos 38° + cos 22° · sin 38°
sin (22° + 38°)
sin 60°
√3 / 2
Case 4
sin 85° · cos 20° - cos 85° · sin 20°
sin (85° - 20°)
sin 65°
0.906
Case 5
cos 12° · cos 10° - sin 12° · sin 10°
cos (12° + 10°)
cos 22°
0.927
Case 6
cos 2x = cos² x - sin² x
cos 2x = [√[1 - (5 / 6)²]² - (5 / 6)²
cos 2x = - 7 / 18
Case 7
cos 2x = cos² x - sin² x
cos 2x = [√[1 - (7 / 9)²]² - (7 / 9)²
cos 2x = - 17 / 81
Case 8
cos 3x = 4 · cos³ x - 3 · cos x
cos 3x = 4 · [√[1 - (7 / 9)²]³ - 3 · [√[1 - (7 / 9)²]
cos 3x ≈ - 0.892
Case 9
cos 6x = cos² 3x - sin² 3x
cos 6x = (4 · cos³ x - 3 · cos x) - (3 · sin x - 4 · sin³ x)
cos 6x = 4 · (cos³ x + sin³ x) - 3 · (cos x + sin x)
cos 6x = 4 · [[√[1 - (4 / 8)²]³+ (4 / 8)³] - 3 · [√[1 - (4 / 8)²] + 4 / 8]
cos 6x = 4 · [(3√3 / 8) + 1 / 8] - 3 · [√3 / 2 + 4 / 8]
cos 6x = 4 · [(1 + 3√3) / 8] - 3 · [(1 + √3) / 2]
cos 6x = - 1
Case 10
cos x = √(1 - sin² x)
cos x = √[1 - (2 / 8)²]
cos x = √15 / 4
To learn more on trigonometric expressions: https://brainly.com/question/11659262
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