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

Question

lisa123 · Answer

cos x - sin ^2x - 1

lisa123 · Answer

Im a bit confused on how solve this problem. Please help!

anonymous · Answer

replace $\sin^2(x)$ by $1-\cos^2(x)$
 don't forget the parentheses

directrix · Answer

cos x - sin ^2x - 1 =
cos x - (1 - cos² x) - 1 =

What next?  @lisa123

lisa123 · Answer

(cosx)( 1+cosx)-2 ????? @Directrix

lisa123 · Answer

No sorry I meant cos x + cos^2x -2

directrix · Answer

cos x - (1 - cos² x) - 1      = cos x - 1 + cos² x - 1    = ?

note the use of the distributive property to simplify - (1 - cos² x)

@lisa123

lisa123 · Answer

-2 + cos^2x+ cosx

directrix · Answer

Question: do you see  how to factor  y ²  + y  - 2  ?

Because I think this is the same type factoring with y as cox x.

directrix · Answer

So, factor this:    y ²  + y  - 2

lisa123 · Answer

y(y+1) -2???

directrix · Answer

No.

 y ² + y - 2  = (y + 2 ) * (y - 1)

directrix · Answer

Now, factor this the same way:

 cos^2x+ cos x - 2

directrix · Answer

( cos x + 2 ) * (cos x - 1)  @lisa123

lisa123 · Answer

Ok I see thank you this helped a lot!

directrix · Answer

You are welcome.