Solution of the equation $$33sin3$$⁡$$x+cos3$$⁡$$x+33sin$$⁡xcos⁡$$x=1$$

Correct option is 1x=nπ+−1nπ6−π6,n∈I

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$Solution of the equation 3 \sqrt{3} \sin^{3} x + \cos^{3} x + 3 \sqrt{3} \sin x \cos x = 1$

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x=nπ+−1nπ6−π6,n∈I

x=2n+1π6,n∈I

x=2nπ+π3,n∈I

x=nπ+−1nπ3,n∈I

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detailed solution

Correct option is A

It is in the form of a3+b3+c3−3abc=0(a+b+c)a2+b2+c2−ab−bc−ca=0,(3sin⁡x)3+(cos⁡x)3+(−1)3−3(3sin⁡x)(cos⁡x)(−1)=03sin⁡x+cos⁡x−1=03sin⁡x+cos⁡x=1, divided by 2sin⁡x+π6=sin⁡π6x+π6=nπ+(−1)nπ6,n∈z

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Solution of the equation 33sin3⁡x+cos3⁡x+33sin⁡xcos⁡x=1

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$Solution of the equation 3 \sqrt{3} \sin^{3} x + \cos^{3} x + 3 \sqrt{3} \sin x \cos x = 1$