Ammarah
  • Ammarah
Identities HELP FINAL TOMORROW
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Ammarah
  • Ammarah
|dw:1433373713959:dw|
Ammarah
  • Ammarah
@perl
perl
  • perl
we should start with the right side?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Ammarah
  • Ammarah
yess
perl
  • perl
$$ \Large { \tan x ( 1 + \cos(2x) )= \\ = \tan x ( 1 + 2\cos^2(x)-1 )= } $$
perl
  • perl
i used the substitution cos(2x) = 2cos^2 x -1
Ammarah
  • Ammarah
how did u get rid of the cosx>
perl
  • perl
$$ \Large { \tan x ( 1 + \cos(2x) ) \\ = \tan x ( 1 + \color{red}{ 2\cos^2(x)-1} ) \\= \tan x \cdot 2\cos^2(x) \\= \frac{\sin x}{\cos x } \cdot 2\cos^2(x) \\~\\= 2 \sin x \cos x \\~\\= \color{blue}{\sin(2x)} } $$
perl
  • perl
the red and blue are substitutions
perl
  • perl
Trig identities: sin(2x) = 2sin x cos x cos(2x) = 2cos^2 x - 1
Ammarah
  • Ammarah
i know but u know u cosx was left
Ammarah
  • Ammarah
how did u get rid of that..
perl
  • perl
in the last line, 2sin x cos x = sin(2x) , thats a trig identity
perl
  • perl
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
perl
  • perl
this is a good resource for identities http://www.purplemath.com/modules/idents.htm
Ammarah
  • Ammarah
ohkk
Ammarah
  • Ammarah
i have another queestion
Ammarah
  • Ammarah
|dw:1433375868645:dw|
perl
  • perl
Is this the question? $$ \Large \csc x = \frac{\cot ( x/2)}{1 + \cos x } $$
Ammarah
  • Ammarah
yes
perl
  • perl
Let's use the half angle identity.
perl
  • perl
tan (x/2) = sin x / ( 1 + cos x )
perl
  • perl
cot(x/2) = 1 / tan(x/2) = ( 1 + cos x ) / sin x
perl
  • perl
thats an equivalent identity
perl
  • perl
cot(x/2) / ( 1 + cos x ) =cot(x/2) * 1 / ( 1 + cos x ) = (1 + cos x ) / sin x * 1 / ( 1 + cos x ) = 1 / sin x = csc x
perl
  • perl
I used this identity http://prntscr.com/7cuud8
Ammarah
  • Ammarah
ok thanks

Looking for something else?

Not the answer you are looking for? Search for more explanations.