Express sin 5x in terms of sin x.

Asked by Kalita Padmanath | 12th Sep, 2016, 11:09: PM

Expert Answer:

begin mathsize 16px style sin 5 straight x equals sin left parenthesis 3 straight x plus 2 straight x right parenthesis
equals sin 3 xcos 2 straight x plus cos 3 xsin 2 straight x
equals left parenthesis 3 sinx minus 4 sin cubed straight x right parenthesis left parenthesis 2 cos squared straight x minus 1 right parenthesis plus left parenthesis 4 cos cubed straight x minus 3 cosx right parenthesis left parenthesis 2 sinxcosx right parenthesis
equals left parenthesis 3 sinx minus 4 sin cubed straight x right parenthesis left square bracket 2 left parenthesis 1 minus sin squared straight x right parenthesis minus 1 right square bracket plus left parenthesis 8 sinxcos to the power of 4 straight x minus 6 sinxcos squared straight x right parenthesis
equals left parenthesis 3 sinx minus 4 sin cubed straight x right parenthesis left square bracket 2 minus 2 sin squared straight x minus 1 right square bracket plus left parenthesis 8 sinx open parentheses cos squared straight x close parentheses squared minus 6 sinx left parenthesis 1 minus sin squared straight x right parenthesis right parenthesis
equals left parenthesis 3 sinx minus 4 sin cubed straight x right parenthesis left square bracket 1 minus 2 sin squared straight x right square bracket plus left parenthesis 8 sinx open parentheses 1 minus sin squared straight x close parentheses squared minus 6 sinx left parenthesis 1 minus sin squared straight x right parenthesis right parenthesis
equals 3 sinx left parenthesis 1 minus 2 sin squared straight x right parenthesis minus 4 sin cubed straight x left parenthesis 1 minus 2 sin squared straight x right parenthesis plus left parenthesis 8 sinx minus 16 sin cubed straight x plus 8 sin to the power of 5 straight x minus 6 sinx plus 6 sin cubed straight x right parenthesis
equals 3 sinx minus 6 sin cubed straight x minus 4 sin cubed straight x plus 8 sin to the power of 5 straight x plus 8 sinx minus 16 sin cubed straight x plus 8 sin to the power of 5 straight x minus 6 sinx plus 6 sin cubed straight x
equals 5 sinx minus 20 sin cubed straight x plus 16 sin to the power of 5 straight x


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Answered by Rebecca Fernandes | 14th Sep, 2016, 11:11: AM