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Question

The general solution of cosx+sinx=cos2x+sin2x is

A
{2nπ}{(2n+1)π6},nZ
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B
{2nπ}{(4n+1)π6},nZ
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C
{(2n+1)π2}{(2n+1)π6},nZ
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D
{(2n+1)π2}{(4n+1)π6},nZ
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Solution

The correct option is B {2nπ}{(4n+1)π6},nZ
cosx+sinx=cos2x+sin2xcosxcos2xsin2x+sinx=0(cosxcos2x)(sin2xsinx)=02sin3x2sinx22cos3x2sinx2=0sinx2(sin3x2cos3x2)=0sinx2=0 or sin3x2cos3x2=0x2=nπx=2nπ,nZsin3x2cos3x2=0sin3x2=cos3x2tan3x2=13x2=nπ+π4x=13(2nπ+π2)x=(4n+1)π6,nZx={2nπ}{(4n+1)π6},nZ

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