Question

Factor the trigonometric equation.
sin^2x-2cosx+7

Answer 1

`\bf \stackrel{\textit{Pythagorean Identities}}{sin^2(\theta)+cos^2(\theta)=1}\implies sin^2(\theta)=1-cos^2(\theta)\\\\-------------------------------\\\\\boxed{sin^2(x)}-2cos(x)+7\implies \boxed{1-cos^2(x)}-2cos(x)+7\\\\\\-cos^2(x)-2cos(x)+8\implies -[\stackrel{\textit{notice this is just }ax^2+bx+c}{cos^2(x)+2cos(x)-8}]\\\\\\-[~~[cos(x)+4][cos(x)-2]~~]\implies [cos(x)+4][2-cos(x)]`