Question

Sin^6(x)=1/4-cos^6(x)

Answer 1

$Sin^6x=frac{1}{4}-Cos^6x$

 

$Sin^6x+Cos^6x=frac{1}{4}$

 

$1-frac{3Sin^22x}{4}=frac{1}{4}$

 

$frac{3Sin^22x}{4}=frac{3}{4}$

 

$Sin^22x=1$

 

$frac{1-Cos4x}{2}=1$

 

$1-Cos4x=2$

 

$Cos4x=-1$

 

4x=±arccos(-1)+2πn=±π+2πn

 

x=±π/4+πn/2