Simplify the expression (sin(x)^2x-sin(x)cos(x))/(xcos(x)) | SnapXam

 Topics

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 Exercise

$\frac{\left(sin^2\right)\left(x\right)-\sin\left(x\right)\cos\left(x\right)}{x\cos\left(x\right)}$

 Step-by-step Solution

 

1

Factor the polynomial $x\sin\left(x\right)^2-\sin\left(x\right)\cos\left(x\right)$ by it's greatest common factor (GCF): $\sin\left(x\right)$

$\frac{\sin\left(x\right)\left(x\sin\left(x\right)-\cos\left(x\right)\right)}{x\cos\left(x\right)}$

 

2

Apply the trigonometric identity: $\frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}$$=\tan\left(\theta \right)$

$\frac{\tan\left(x\right)\left(x\sin\left(x\right)-\cos\left(x\right)\right)}{x}$

 Why is sin(x)/cos(x) = tan(x) ?

Final answer to the exercise  

$\frac{\tan\left(x\right)\left(x\sin\left(x\right)-\cos\left(x\right)\right)}{x}$

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 Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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