Question

8.) Simplify.

Answer 1

Answer:

The answer to your question is letter E. cos²α

Step-by-step explanation:

                     

                            cot²Ф  - cot²Фcos²Ф

Remember that    cot = $\frac{cos \alpha}{sin \alpha }$ ; substitute in the previous equation

                            $\frac{cos^{2}\alpha }{sin^{2} \alpha} - \frac{cos^{2}\alpha }{sin^{2}\alpha } cos^{2}\alpha$

                                 $\frac{cos^{2}\alpha - cos^{4}\alpha }{sin^{2}\alpha }$                     Factor  cos²α

                                $\frac{cos^{2}\alpha(1 - cos^{2}\alpha }{sin^{2}\alpha }$

Remember that   sin²α = 1 - cos²α

                                $\frac{cos^{2}\alpha sin^{2}\alpha}{sin^{2} \alpha}$

Simplify

                              cos²α