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Can you prove this identity of cos(4x)=1-8sin2x+8sin2x ?

Esteban Garcia , 8 Years ago
Grade 12th pass
anser 1 Answers
Nandana

Last Activity: 8 Years ago

hi,
 I think it’s not  “1-8 sin2 x + 8 sin2 x “  = 1 , it is
               ‘ 1- 8 sin2 x cos2 x ‘ , the proof is this way –
                      cos (4x) = cos (2x+2x) = cos2 (2x) – sin2 (2x)
                                                    = [cos2 (x) – sin2 (x) ]2 – (2 sin(x) cos (x)) 2
                                                   = cos4 x + sin4 x – 2 cos2 (x) sin2 (x) – 4 sin2 x cos2 x
                                                   = cos4 x + sin4 x -6 cos2 (x) sin2 (x)
                                                   = cos4 x + sin4 x +2 cos2 (x) sin2 (x) -2 cos2 (x) sin2 (x)-6 cos2 (x) sin2 (x)
                                                   =(cos2 x + sin2 x)2 – 8 cos2 (x) sin2 (x)
                                                   = 1- 8 cos2 (x) sin2 (x)
                                                                                                     thank you !
     

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