Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
cos(2x)−cos(x)
Evaluate
2cos2(x)−cos(x)−1
Transform the expression
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Evaluate
2cos2(x)
Use cos2t=1−sin2t to transform the expression
2(1−sin2(x))
Use the the distributive property to expand the expression
2×1+2(−sin2(x))
Any expression multiplied by 1 remains the same
2+2(−sin2(x))
Multiply the terms
2−2sin2(x)
2−2sin2(x)−cos(x)−1
Subtract the numbers
1−2sin2(x)−cos(x)
Transform the expression
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Evaluate
−2sin2(x)
Use sin2t=1−cos2t to transform the expression
−2(1−cos2(x))
Use the the distributive property to expand the expression
−2×1−2(−cos2(x))
Any expression multiplied by 1 remains the same
−2−2(−cos2(x))
Multiply the terms
−2+2cos2(x)
1−2+2cos2(x)−cos(x)
Subtract the numbers
−1+2cos2(x)−cos(x)
Transform the expression
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Evaluate
2cos2(x)
Use 2cos2t=cos(2t)+1 to transform the expression
2×21+cos(2x)
Cancel out the common factor 2
1×(1+cos(2x))
Multiply the terms
1+cos(2x)
−1+1+cos(2x)−cos(x)
Solution
cos(2x)−cos(x)
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Factor the expression
(cos(x)−1)(2cos(x)+1)
Evaluate
2cos2(x)−cos(x)−1
Rewrite the expression
2cos2(x)+(1−2)cos(x)−1
Calculate
2cos2(x)+cos(x)−2cos(x)−1
Rewrite the expression
cos(x)×2cos(x)+cos(x)−2cos(x)−1
Factor out cos(x) from the expression
cos(x)(2cos(x)+1)−2cos(x)−1
Factor out −1 from the expression
cos(x)(2cos(x)+1)−(2cos(x)+1)
Solution
(cos(x)−1)(2cos(x)+1)
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