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26 November, 04:57

Sin x+sin 5x = cot 2x

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  1. 26 November, 06:48
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    Step-by-step explanation:

    sinx+sin (x+4x) = cot2x sinx+sinx cos4x+cosx sin4x=cot2x

    sinx+sinx cos4x=sinx (1+cos4x) =

    sinx (1-1+2 (cos2x) ^2) = 2sinx (cos2x) ^2

    sin4x=2sin2xcos2x

    2sinx (cos2x) ^2+cosx+2sin2xcos2x=cot2x

    2sinxcos2x (cos2x+2 (cosx) ^2) = cot2x

    but 2 (cosx) ^2=cos2x+1

    2sinxcos2x (cos2x+cos2x+1) = cos2x/sin2x

    (2sinxsin2x) (2cos2x+1) = 1

    (4cosx (sinx) ^2) (2cos2x+1) = 1
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