Math  /  Trigonometry

QuestionRewrite 5cos4x5 \cos 4 x in terms of cosx\cos x. \square

Studdy Solution
Multiply the entire expression by 5 to rewrite 5cos4x 5 \cos 4x :
5cos4x=5(8cos4x8cos2x+1) 5 \cos 4x = 5(8 \cos^4 x - 8 \cos^2 x + 1) 5cos4x=40cos4x40cos2x+5 5 \cos 4x = 40 \cos^4 x - 40 \cos^2 x + 5
The expression 5cos4x 5 \cos 4x in terms of cosx \cos x is:
40cos4x40cos2x+5 \boxed{40 \cos^4 x - 40 \cos^2 x + 5}

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