Question

C1. (корень из 3)^2sin 2x=(3)^корень2sinx

Answer 1

$( sqrt{3} )^{2sin2x}=3^{ sqrt{2} sin x} \ \ sin 2x= sqrt{2} sin x \ \ 2sin xcos x-sqrt{2}sin x=0 \ \ sin x(2cos x-sqrt{2})=0 \ \ sin x=0 \ \ x_1= pi k, k in Z \ \ cos x= frac{sqrt{2}}{2}$

$x_2=pm frac{ pi }{4} +2 pi n, n in Z$

Answer 2

$( sqrt{3} ) ^{2sin2x} =3 ^{ sqrt{2} sinx}$
sin2x=√2sinx
2sinxcosx-√2sinx=0
2sinx(cosx-√2/2)=0
sinx=0⇒x=πn
cosx=√2/2⇒x=+-π/4+2πn