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trig

 Apr 25, 2019
 #1
avatar+105277 
+2

1 - tan^2x           cos^2x/cos^2x  - sin^2x/cos^2x          [ cos^2x - sin^2x ] * cosx

________  =  ____________________________ =  _____________________  =

  2 tan x                   2 sinx / cosx                                    2sinx *cos^2 x

 

 

cos^2x - sin^2x            cos 2x

____________  =  _________   =   cot2x  =  1 / tan2x     ⇒    Identity

  2sinxcosx                  sin2x

 

 

cool cool cool

 Apr 25, 2019
 #2
avatar+105277 
+2

(sin x - cos x)^2  =   sin^2x  - 2sinxcosx  + cos^2x  =  sin^2x + cos^2x  - 2sinxcosx   =  1 - sin 2x 

 

Not an identity

 

The third one is an identity  because

 

sin (8x)  =  sin (2 * 4x)  =  2sin4xcos4x

 

 

cool cool cool

 Apr 25, 2019
 #3
avatar+105277 
+1

WolframAlpha shows the last to be an identity.....but.....I don't know how to verify it..[it may be lengthy]...maybe someone else does

 

cool cool cool

 Apr 25, 2019

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