Sin ^6x + Cos ^6x Lies Between - Toppr

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIIMathsQuestionsin6x+cos6x lies between
  1. 14 and 1
  2. None of these
  3. 14 and 2
  4. 0 and 1
A0 and 1B14 and 2CNone of theseD14 and 1Open in AppSolutionVerified by Toppr

We have sin6x+cos6x=(sin2x)3+(cos2x)3=(sin2x+cos2x)3−3sin2xcos2x(sin2x+cos2x)=1−3sin2xcos2x=1−34.4sin2xcos2x=1−34(sin2x)2⇒ Maximum value of sin6x+cos6x is 1−34×0=1 and minimum values is 1−34×1=14

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If the lines x−12=y+13=z−14 and x−31=y−k1=z1 and intersect, then k = [IIT Screening 2004]

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