Question

Help???
(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x

Answer 1

(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x
sinx*((sinx/cosx)*cosx-(cosx/sinx)*cos)=1-2cos2x
sinx*(sinx-cos^2x/sinx)=1-2cos2x
sin^2x-cos^2x=1-2(cos^2x-sin^2x)
sin^2x-cos^2x+2(cos^2x-sin^2x)=1
cos^2x-sin^2x=1
cos2x=1
I think you should know how to continue :)

Answer 2

So when we use the quotient identities for tan x and cot x, they cancel thmselves out, right?

Answer 3

Okay, so they don't cancel out, but how did you get (sin)(sin-cos^2/sin)? @purger

Answer 4

Do you get what he did @Isaiah.Feynman ?

Answer 5

tanx=sinx/cosx, ctgx=cosx/sinx, so i multiplied fractions like theye are numbers :)

Answer 6

Yeah, pretty straight forward. I didn't look at every detail, but experience tells me its not that bad.

Answer 7

Oh, I got it now. I had my imaginary parenthesis in the wrong places. :) Thanks guys! God bless!

Answer 8

Wait, I think you were trying to do the wrong thing.. I just have to make the left side look like the right. So I don't do anything to the right side.. How do I get sin^2 x - cos^2 x to equal 1 -2cos^2 x??

Answer 9

but you cannot make left side look like right, because they are not equal...
LS: -cos2x
RS:1-2cos2x

and thats not equal!

Answer 10

oh thats cos^2(x) like exponent 2?

Answer 11

(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2x
sinx*((sinx/cosx)*cosx-(cosx/sinx)*cos)=1-2cos^2x
sinx*(sinx-cos^2x/sinx)=1-2cos^2x
sin^2x-cos^2x=1-2cos^2x
(1-cos^2x) -cos^2x=1-2cos^2x
Q.E.D.

Answer 12

Oh, okay. Awesome. That makes much more sense. How do you guys know when those things equal eachother? Like sin^2x equaling (1-cos^2x)?

Answer 13

sin^2x+cos^2x=1 - its main identity in trigonometry... from that folows sin^2x=1-cos^2x

Answer 14

How does multiplying this --> (1-cos^2x) -cos^2x turn into the right side? Wouldn't you distribute that?

Answer 15

there is no multiplication... :) (1-cos^2x)-cos^2x=1-cos^2x-cos^2x=1-2cos^2x :)

Answer 16

Oops.. I'm an idiot. Haha. :p So they just cancel out?

Answer 17

Why wouldn't it become a negative? Because they are both negative?

Answer 18

imagine that cos^2x=t then 1-t-t=1-2t. what you want to cancel?

Answer 19

Oh my gosh. I really need to pay attention more. The right side IS a negative. I am really slow today.

Answer 20

Thank you so much. I don't know why it took me so long to catch on. God bless you!