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

 Exercise

$\frac{cos^2\left(a\right)\:-3cos\left(a\right)\:+2}{sin^2\left(a\right)}$

 

Factor the trinomial $\cos\left(a\right)^2-3\cos\left(a\right)+2$ finding two numbers that multiply to form $2$ and added form $-3$

$\begin{matrix}\left(-1\right)\left(-2\right)=2\\ \left(-1\right)+\left(-2\right)=-3\end{matrix}$

 

Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

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

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

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