How do you find all values of x in the interval [0, 2pi] in the equation $cos x =sin 2x$ ?

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Answer 1 · 2016-04-17T07:44:32

$S={pi/6, pi/2, (5pi)/6, (3pi)/2}$

$cosx - sin 2x =0$

$cosx - 2sin x cos x=0$

$cosx(1-2sinx)=0$

$cos x=0 or 1-2sinx =0$

$x=cos^-1 0 or -2sinx=-1-> sinx= 1/2-> x=sin^-1(1/2)$

$x=pi/2 , (3pi)/2 or x=pi/6 , (5pi)/6$

$S={pi/6, pi/2, (5pi)/6, (3pi)/2}$

How do you find all values of x in the interval [0, 2pi] in the equation cos x =sin 2xcos x =sin 2x?