Question

Identities HELP FINAL TOMORROW

Answer 1

@perl

Answer 2

we should start with the right side?

Answer 3

yess

Answer 4

$$ \Large {
\tan x ( 1 + \cos(2x) )=
\\ = \tan x ( 1 + 2\cos^2(x)-1 )=


}
$$

Answer 5

i used the substitution
cos(2x) = 2cos^2 x -1

Answer 6

how did u get rid of the cosx>

Answer 7

$$ \Large {
\tan x ( 1 + \cos(2x) )
\\ = \tan x ( 1 + \color{red}{ 2\cos^2(x)-1} )
\\= \tan x \cdot 2\cos^2(x)
\\= \frac{\sin x}{\cos x } \cdot 2\cos^2(x)
\\~\\= 2 \sin x \cos x
\\~\\= \color{blue}{\sin(2x)}
}
$$

Answer 8

the red and blue are substitutions

Answer 9

Trig identities:
sin(2x) = 2sin x cos x
cos(2x) = 2cos^2 x - 1

Answer 10

i know but u know u cosx was left

Answer 11

how did u get rid of that..

Answer 12

in the last line, 2sin x cos x = sin(2x) , thats a trig identity

Answer 13

You can prove that by use of the addition formula:
sin(2x) = sin(x+x) = sin x cos x + cos x sin x = 2 sin x cos x

Answer 14

this is a good resource for identities http://www.purplemath.com/modules/idents.htm

Answer 15

ohkk

Answer 16

i have another queestion