Question

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

\(\large cos~x~ -~ sin^2x - 1\)

Answer 1

@phi

Answer 2

i think they want you to use sin^2 + cos^2 = 1
to get rid of the sin^2 (replace it with 1 - cos^2 )

Answer 3

So, \(\cos x + 1 - \cos^2\)?

Answer 4

close. check your algebra

Answer 5

cos x - (1 - cos^2 x ) - 1

Answer 6

distribute the -1.
after you simplify, you have a "quadratic" that you can factor.

Answer 7

cosx-1+cos^2 x -1?

Answer 8

ok, but you can combine -1 - 1
and it's always good to put it in "standard order" so make cos^2 x the first term

Answer 9

Ok, \(\cos^2x+\cos x-2\)

Answer 10

yes. now let's rename cos(x) as y. this makes the expression
\[ y^2 + y -2 \]
can you factor that ?
(yes you can!)

Answer 11

(y + ) (y - )
look at the 2 and list its factors: 1,2 (only choice)
they have different signs, and the larger one will be +

Answer 12

you should get
(y+2)(y-1)

or, putting cos x back in
(cos x +2)( cos x -1)

Answer 13

Thank you!