Question

Prove that cos^3x + cos^3 (120 + x) + cos^3(120- x) = cos 3x.
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Answer 1

Answer:

Step-by-step explanation:

cos3x + cos3(120 − x) + cos3(120 + x)

= cos 3x + 3 cos x4 + cos (360 − 3x) + 3 cos (120 − x)4 + cos (360 + 3x) + 3 cos (120 + x)4

= 14 [cos 3x + 3 cos x + cos 3x + 3 cos (120 − x) + cos 3x + 3 cos (120 + x)]

= 34 [cos 3x + cos x + cos (120 − x) + cos (120 + x)]

= 34 [2 cos 2x cos x + 2 cos 120 cos x]

= 34 [2 cos 2x cos x + 2 × (−12) cos x]

= 34 [2 cos 2x cos x − cos x]

= 34 [cos 3x + cos x − cos x]

= 34 [cos 3x]

Maximum value of cos 3x = 1So maximum value of cos3x + cos3(120 − x) + cos3(120 + x) = 34 × 1 = 34