KronosH24908 KronosH24908
  • 03-11-2022
  • Mathematics
contestada

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

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PallasH688745 PallasH688745
  • 03-11-2022

You use the next trigonometric inentities:

[tex]\begin{gathered} \sin ^2x+\cos ^2x=1 \\ \\ \sin ^2x=1-\cos ^2x \end{gathered}[/tex][tex]\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}[/tex]

Common factor cosx:

[tex]=\cos x(1+\cos x)-2[/tex]

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