Posted by **v** on Monday, December 3, 2012 at 11:52pm.

can i use factoring to simplify this trig identity?

the problem is sinx + cotx * cosx i know the answer is cscx and i know how to get it but i want to know if i can do factoring to get it bc i tried to but it wont give me the answer .

this is the step i went through:

1) sinx + cotx * cosx turns into sinx +(cosx/sinx)*cosx

2) i try to factor out sinx so that i would get sinx(1+ cosx * cosx)

3) that left me with sinx(1+cos^(2) x) that's where i im lost can anyone enlighten me plz

- trigonometry -
**Steve**, Monday, December 3, 2012 at 11:54pm
cot = cos/sin, so you have

sin + cos^2/sin

= (sin^2+cos^2)/sin

= 1/sin

= csc

- trigonometry -
**v**, Monday, December 3, 2012 at 11:56pm
im well aware of that steve thank you for answering but i really wanted to know was is it at all possible to use factoring to solve this like i have up there

- trigonometry -
**Steve**, Tuesday, December 4, 2012 at 12:17am
I don't see any way to use factoring. You don't in fact come up with

sin(1+cos^2)

because you have that pesky 1/sin under the cos^2.

If you try to fractor out the sin, you get

sin(1+cos^2/sin^2)

and again you end up with sin^2+cos^2 on top.

- trigonometry -
**Reiny**, Tuesday, December 4, 2012 at 7:51am
We could do some " silly" factoring

sinx + (cosx/sinx)(cosx)

= sinx + cos^2 x (sinx)^-1

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

= (sinx)^-1

= 1/sinx

= cscx

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