Question

Can someone show all steps necessary to verify the trigonometric identity? I don't really know how to do it on my own. Thanks!

1 - 2cos^2x = 2sin^2x - 1

Answer 1

\[1-2\cos^2x = 2\sin^2x -1\]

Answer 2

In case it didn't make sense the first time?

Answer 3

use \(\huge \color{red}{\sin^2 x+\cos^2x=1}\)

Answer 4

I honestly have no idea how....

Answer 5

ok. from that
\(\huge \color{red}{\sin^2 x=1-\cos^2x}\)
so substitute this for sin^2 x on right side.
what u get ?
2(...?...)-1

Answer 6

got that ^ ?

Answer 7

Do you get cos^2x?

Answer 8

lets see what we get
right side = 2sin^2 x -1
=\(\huge \color{red}{2(1-\cos^2x)-1}\)
=..... ?
can u tell me next step ?

Answer 9

so it would be 2-2cos^2x -1 which would end up being 1-2cos^2x
Right..? & Thank you!

Answer 10

absolutely correct :)

Answer 11

and
\[ \begin{array}l\color{red}{\text{w}}\color{orange}{\text{e}}\color{#e6e600}{\text{l}}\color{green}{\text{c}}\color{blue}{\text{o}}\color{purple}{\text{m}}\color{purple}{\text{e}}\color{red}{\text{ }}\color{orange}{\text{^}}\color{#e6e600}{\text{_}}\color{green}{\text{^}}\color{blue}{\text{}}\end{array} \]

Answer 12

& That was on our right side, so now they equal each other! Yay! :) How did you know to use the sin^2x + cos^2x=1? I know that not squared they equal 1, but even when they are squared they equal 1? Does my question make sense?

Answer 13

I meant I knew without the 2 in front of them they equaled 1.

Answer 14

Like that I knew it equaled 1

Answer 15

no, your Q didn't make sense to me, sorry.

Answer 16

that is squared..

Answer 17

Hmm. let me try again. So no matter the coefficent attatched to the front of sin^2theta _ cos^2theta, the answer is one?

Answer 18

I meant coefficient not squared... Whoops!

Answer 19

Dang it! I meant + not _

Answer 20

no, the co=efficients would matter.
if they are different , it will not be =1
but if the co-efficient are same, we can factor out that co-efficient, then it =1
like example
asin^2x+bcos^2x is not 1
but
asin^2x+acos^2x = a(1)

Answer 21

Ohh okay, I get it now. Thank you! & sorry for confusing you!

Answer 22

no problem :)