Question

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

cos x - sin^2 x - 1

Answer 1

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

Answer 2

how would i set that up?

Answer 3

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

Answer 4

so i would get cosx-2

Answer 5

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

Answer 6

so it would be y(y-2)

Answer 7

how?

Answer 8

I factored it...

Answer 9

can you show me the steps?

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

yeah..replace y with cos x

Answer 14

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

Answer 15

Thank you

Answer 16

right...u r welcome..