anonymous
  • anonymous
sin 4x = 4 sin x cos³x-4sin³x cos x. Show as an identity.
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
2sin2xcos2x = 4sinxcosx(cos^2 x - sin^2 x)
anonymous
  • anonymous
thats sin4x
anonymous
  • anonymous
skipped a few steps there , I see what you have done, but to someone asking the question it is unlikely they will be able to follow

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anonymous
  • anonymous
i assume they know basic trig ratios
anonymous
  • anonymous
Have difficulty doing these, could you help with the steps so I can try and understand
anonymous
  • anonymous
sin(2a) = 2sin(a)cos(x)
anonymous
  • anonymous
cos(2a) = cos^2 (a) - sin^2 (a)
anonymous
  • anonymous
remember them
anonymous
  • anonymous
now sin(4x) = sin( 2 * 2x) = 2sin(2x)cos(2x) by applying the first formula once
anonymous
  • anonymous
hard to memorize, I see those in my notes. Thanks for helping
anonymous
  • anonymous
now we can apply the first formula again to sin(2x) , to get 2sin(x)cos(x) and we apply the second formula to the cos(2x) term to get cos^2 (x) - sin^2 (x)
anonymous
  • anonymous
so sin(4x) = 2 * ( 2sin(x)cos(x) ) ( cos^2 (x) - sin^2(x) )
anonymous
  • anonymous
= 4sin(x)cos(x) ( cos^2(x) - sin^2(x)) , then expand
anonymous
  • anonymous
thank you!

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