Simplify the trigonometric expression (sin(2y)sin(y))/(cos(y)-cos(y)^3)

 Exercise

$\frac{\sin\left(2y\right)siny}{\cos\left(y\right)-cos^3\left(y\right)}$

 

Factor the polynomial $\cos\left(y\right)-\cos\left(y\right)^3$ by it's greatest common factor (GCF): $\cos\left(y\right)$

$\frac{\sin\left(2y\right)\sin\left(y\right)}{\cos\left(y\right)\left(1-\cos\left(y\right)^2\right)}$

 

Apply the trigonometric identity: $1-\cos\left(\theta \right)^2$$=\sin\left(\theta \right)^2$, where $x=y$

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

 Why is 1 - cos(x)^2 = sin(x)^2 ?

 

Simplify the fraction by $\sin\left(y\right)$

$\frac{\sin\left(2y\right)}{\cos\left(y\right)\sin\left(y\right)}$

$\frac{\sin\left(2y\right)}{\cos\left(y\right)\sin\left(y\right)}$

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