OpenStudy (anonymous):

Factor the algebraic expression below in terms of a single trigonometric function. cos x - sin^2 x - 1

4 years ago
OpenStudy (souvik):

sin^2x=1-cos^2x suppose y=cosx and try to factor it

4 years ago
OpenStudy (anonymous):

how would i set that up?

4 years ago
OpenStudy (souvik):

cosx-sin^2x-1 =cosx-(1-cos^2x)-1 =cosx-1+cos^2x-1 =cos^2x+cosx-2

4 years ago
OpenStudy (anonymous):

so i would get cosx-2

4 years ago
OpenStudy (souvik):

now replace cosx by y ... so y^2+y-2 now you can factor it

4 years ago
OpenStudy (anonymous):

so it would be y(y-2)

4 years ago
OpenStudy (souvik):

how?

4 years ago
OpenStudy (anonymous):

I factored it...

4 years ago
OpenStudy (souvik):

can you show me the steps?

4 years ago
OpenStudy (anonymous):

y^2+y+2 -->y is common factor --> y(y+2)

4 years ago
OpenStudy (souvik):

no.. y^2+y-2 =y^2+2y-y-2 =y(y+2)-1(y+2) =(y+2)(y-1) got it?

4 years ago
OpenStudy (anonymous):

oh duh. Yeah i got it. Would i then replace the y with cosx again or just leave it as y?

4 years ago
OpenStudy (souvik):

yeah..replace y with cos x

4 years ago
OpenStudy (anonymous):

so the final answer would be (cosx+2) (cosx-1)

4 years ago
OpenStudy (anonymous):

Thank you

4 years ago
OpenStudy (souvik):

right...u r welcome..

4 years ago
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