Question

8.) Simplify.

cot^2 0 - cot ^2 0 cos ^2 0
A.) tan^2 0
B.) -1
C.) 3
D.) sin ^2 0
E.) cos^2 0

Answer 1

The answer to your question is letter E. cos²α

Explanation:

cot²Ф - cot²Фcos²Ф

Remember that cot =
`(cos \alpha)/(sin \alpha )` ; substitute in the previous equation

`(cos^(2)\alpha )/(sin^(2) \alpha) - (cos^(2)\alpha )/(sin^(2)\alpha ) cos^(2)\alpha`

`(cos^(2)\alpha - cos^(4)\alpha )/(sin^(2)\alpha )` Factor cos²α

`(cos^(2)\alpha(1 - cos^(2)\alpha )/(sin^(2)\alpha )`

Remember that sin²α = 1 - cos²α

`(cos^(2)\alpha sin^(2)\alpha)/(sin^(2) \alpha)`

Simplify

cos²α