Math  /  Trigonometry

QuestionUse the sum-to-product formulas to find the exact value of the expression. 9cos120+9cos609 \cos 120^{\circ}+9 \cos 60^{\circ}
Step 1 Factor out the constant. 9cos120+9cos60=9 \cos 120^{\circ}+9 \cos 60^{\circ}= \square (cos120+cos60)\left(\cos 120^{\circ}+\cos 60^{\circ}\right)

Studdy Solution
Simplify the expression using known cosine values:
cos(90)=0 \cos (90^{\circ}) = 0
Thus,
2cos(90)cos(30)=2×0×cos(30)=0 2 \cos (90^{\circ}) \cos (30^{\circ}) = 2 \times 0 \times \cos (30^{\circ}) = 0
Therefore, the expression becomes:
9×0=0 9 \times 0 = 0
The exact value of the expression is:
0 \boxed{0}

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