Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−sin(3x)
Evaluate
sin3(x)−3sin(x)cos2(x)
Transform the expression
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Evaluate
sin3(x)
Use sin2t=1−cos2t to transform the expression
sin(x)(1−cos2(x))
Apply the distributive property
sin(x)×1+sin(x)(−cos2(x))
Any expression multiplied by 1 remains the same
sin(x)+sin(x)(−cos2(x))
Multiply the terms
sin(x)−sin(x)cos2(x)
sin(x)−sin(x)cos2(x)−3sin(x)cos2(x)
Subtract the terms
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Evaluate
−sin(x)cos2(x)−3sin(x)cos2(x)
Rewrite the expression
−cos2(x)sin(x)−3cos2(x)sin(x)
Collect like terms by calculating the sum or difference of their coefficients
(−1−3)cos2(x)sin(x)
Subtract the numbers
−4cos2(x)sin(x)
sin(x)−4cos2(x)sin(x)
Transform the expression
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Evaluate
−4cos2(x)sin(x)
Use cos2t=1−sin2t to transform the expression
−4(1−sin2(x))sin(x)
Multiply the terms
−4sin(x)(1−sin2(x))
sin(x)−4sin(x)(1−sin2(x))
Use 1−sin2(t)=cos2(t) to transform the expression
sin(x)−4sin(x)cos2(x)
Transform the expression
sin(x)−sin(3x)−sin(x)
The sum of two opposites equals 0
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Evaluate
sin(x)−sin(x)
Collect like terms
(1−1)sin(x)
Add the coefficients
0×sin(x)
Calculate
0
0−sin(3x)
Solution
−sin(3x)
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Factor the expression
(sin2(x)−3cos2(x))sin(x)
Evaluate
sin3(x)−3sin(x)cos2(x)
Rewrite the expression
sin2(x)sin(x)−3cos2(x)sin(x)
Solution
(sin2(x)−3cos2(x))sin(x)
Show Solution