Question

$\frac{co{s}^2\Theta -3cos\Theta +2}{si{n}^2\Theta }$

Answer 1

We have,

$\frac{{\cos }^2\theta -3\cos \theta +2}{{\sin }^2\theta }$

$\Rightarrow \frac{{\cos }^2\theta -2\cos \theta -\cos \theta +2}{{\sin }^2\theta }$

$\Rightarrow \frac{\cos \theta (\cos \theta -2)-1(\cos \theta -2)}{{\sin }^2\theta }$

$\Rightarrow \frac{(\cos \theta -2)(\cos \theta -1)}{{\sin }^2\theta }$

$\Rightarrow \frac{(\cos \theta -2)(\cos \theta -1)}{(1-{\cos }^2\theta )}$

$\Rightarrow \frac{(\cos \theta -2)(\cos \theta -1)}{(1-\cos \theta )(1+\cos \theta )}$

$\Rightarrow \frac{-(\cos \theta -2)}{(1+\cos \theta )}$

$\Rightarrow \frac{(2-\cos \theta )}{(1+\cos \theta )}$

Hence this is the answer.