Question

DOES ANYONE KNOW HOW TO SOLVW THESE>???
#1) cos x(sec x – cos x)
#2) (1 + cot x)^2

Answer 1

i think you were asked to use distributive property here.

Answer 2

yes

Answer 3

for number 1, in distributing, note that, secx and cosx are reciprocal of are other.

Answer 4

so, cosx*(secx) = ____?

Answer 5

you have

\[\cos(x)(\frac{1}{\cos(x)} - \cos(x)) = 1 - \cos^2(x) = \sin^2(x)\]

Answer 6

this is a binomial expansion of a perfect square

\[(1 + \cot(x))^2 = 1 + 2\cot(x) + \cot^2(x)\]

use

\[\cos^2(x) + 1 = \csc^2(x)\]

so the solution is

\[\csc^2(x) + 2\cot(x)\]