Question

cosx-sin^2x-1how do I write the expression in factored form as an algebraic expression of a single trigometric function?

Answer 1

You use the next trigonometric inentities:

`\begin{gathered} \sin ^2x+\cos ^2x=1 \\ \\ \sin ^2x=1-\cos ^2x \end{gathered}`
`\begin{gathered} \cos x-\sin ^2x-1 \\ \\ =\cos x-(1-\cos ^2x)-1 \\ =\cos x-1+\cos ^2x-1 \\ =\cos x+\cos ^2x-2 \\ \end{gathered}`

Common factor cosx:

`=\cos x(1+\cos x)-2`