Question

Factor the algebraic expression below in terms of a single trigonometric function.

cos x - sin^2 x - 1

Answer 1

you can do this because of sin^2x-1

we know that cos^2x+sin^2x=1

to convert we use the sinx and 1 portion

will finish on next line

Answer 2

Therefore

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

Answer 3

Does this make sense?

So your single equation becomes

\[\cos (x)-\cos^2(x)\]

Answer 4

Do you need to take the equation further or no?

Answer 5

This makes a lot more sense now, thank you. So really its all based of the Pythagorean Identity Sin^2x+Cos^2x=1?

Answer 6

Exactly!