Question

simplify the following
cosx (tanx+cotx)

Answer 1

the definitions of tangent/cotangent are what?

Answer 2

i know that tan = sin/cos and that cot= cos/ sin but i dont know where to go from there

Answer 3

plug them in, then distribute cos(x) to both terms

Answer 4

so i get sin + 2cos/sin ?

Answer 5

because the cos cancels out in the first one right?

Answer 6

does cos x * cos x = 2cos x?

Answer 7

sorry cos^2

Answer 8

yep. so you have sin x + cos^2x/sin x. personally i think writing this as sin(x) + cos(x)*ctn(x) is simpler, so that's what i would submit.

Answer 9

thanks

Answer 10

if cos^2=1-sin^2 does that change my answer

Answer 11

um i guess you could do that. you could do:
cos^2x/sinx = (1-sin^2x)/sin x = 1/sinx - sinx = csc x - sin x
and into the original:
sin x + csc x - sin x
= csc x
That's the simplest way, I didn't see that

Answer 12

thanks

Answer 13

Or we could even write it as

\[\large cos(x)(tan(x) + cot(x))\]
\[\large cos(x)(\frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)})\]
\[\large \frac{\cancel{(cos)(x)}sin(x)}{\cancel{cos(x)}} + \frac{cos^2(x)}{sin(x)}\]
\[\large sin(x) + \frac{1 - sin^2(x)}{sin(x)}\]
\[\large sin(x) + \frac{1}{sin(x)} - \frac{sin^2(x)}{sin(x)}\]
\[\large \cancel{sin(x)} + csc(x) \cancel{- sin(x)}\]
\[\large csc(x)\]

Answer 14

ahh beat me to it :) lol Great job you two!

Answer 15

nice latex skills. the reason i gave up on it is because it makes me slow to reply. gj to you

Answer 16

thanks so much to both of you

Answer 17

really quick in this problem because it is addition i cannot cross each side out correct?

Answer 18

Correct

Answer 19

okay thats what i thought i just wanted to make sure that it wasn't making it harder than it needed to be