Question

Уравнение :cosx = sin3x
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Answer 1

$cos x = sin (3x)\\sinbigg(dfrac {pi}2-xbigg)-sin (3x)=0\\2sinbigg(dfrac{frac{pi}2-x-3x}2bigg)cosbigg(dfrac{frac{pi}2-x+3x}2bigg)=0\\2sinbigg(dfrac{pi}4-2xbigg)cosbigg(dfrac{pi}4+xbigg)=0\\1)~sinbigg(dfrac{pi}4-2xbigg)=0;~~~~dfrac{pi}4-2x=pi n;~nin mathbb Z\\~~~~2x=dfrac{pi}4-pi n;~~~~boxed{boldsymbol{x_1=dfrac{pi}8+dfrac{pi k}2,~~~kinmathbb Z}}\\\2)~cosbigg(dfrac{pi}4+xbigg)=0;~~~~dfrac{pi}4+x=dfrac {pi}2+pi m$

$~~~~~~~~boxed{boldsymbol{x_2=dfrac{pi}4+pi m,~~~minmathbb Z}}$