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Ammarah
 one year ago
Identities HELP FINAL TOMORROW
Ammarah
 one year ago
Identities HELP FINAL TOMORROW

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perl
 one year ago
Best ResponseYou've already chosen the best response.4we should start with the right side?

perl
 one year ago
Best ResponseYou've already chosen the best response.4$$ \Large { \tan x ( 1 + \cos(2x) )= \\ = \tan x ( 1 + 2\cos^2(x)1 )= } $$

perl
 one year ago
Best ResponseYou've already chosen the best response.4i used the substitution cos(2x) = 2cos^2 x 1

Ammarah
 one year ago
Best ResponseYou've already chosen the best response.1how did u get rid of the cosx>

perl
 one year ago
Best ResponseYou've already chosen the best response.4$$ \Large { \tan x ( 1 + \cos(2x) ) \\ = \tan x ( 1 + \color{red}{ 2\cos^2(x)1} ) \\= \tan x \cdot 2\cos^2(x) \\= \frac{\sin x}{\cos x } \cdot 2\cos^2(x) \\~\\= 2 \sin x \cos x \\~\\= \color{blue}{\sin(2x)} } $$

perl
 one year ago
Best ResponseYou've already chosen the best response.4the red and blue are substitutions

perl
 one year ago
Best ResponseYou've already chosen the best response.4Trig identities: sin(2x) = 2sin x cos x cos(2x) = 2cos^2 x  1

Ammarah
 one year ago
Best ResponseYou've already chosen the best response.1i know but u know u cosx was left

Ammarah
 one year ago
Best ResponseYou've already chosen the best response.1how did u get rid of that..

perl
 one year ago
Best ResponseYou've already chosen the best response.4in the last line, 2sin x cos x = sin(2x) , thats a trig identity

perl
 one year ago
Best ResponseYou've already chosen the best response.4You 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
 one year ago
Best ResponseYou've already chosen the best response.4this is a good resource for identities http://www.purplemath.com/modules/idents.htm

Ammarah
 one year ago
Best ResponseYou've already chosen the best response.1i have another queestion

perl
 one year ago
Best ResponseYou've already chosen the best response.4Is this the question? $$ \Large \csc x = \frac{\cot ( x/2)}{1 + \cos x } $$

perl
 one year ago
Best ResponseYou've already chosen the best response.4Let's use the half angle identity.

perl
 one year ago
Best ResponseYou've already chosen the best response.4tan (x/2) = sin x / ( 1 + cos x )

perl
 one year ago
Best ResponseYou've already chosen the best response.4cot(x/2) = 1 / tan(x/2) = ( 1 + cos x ) / sin x

perl
 one year ago
Best ResponseYou've already chosen the best response.4thats an equivalent identity

perl
 one year ago
Best ResponseYou've already chosen the best response.4cot(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
 one year ago
Best ResponseYou've already chosen the best response.4I used this identity http://prntscr.com/7cuud8
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