Question 403218
{{{cos2w+3cosw -1=0}}}
Use FORMULA {{{cos2w=(cosw)^2-(sinw)^2}}}
{{{cos2w+3cosw -1=0}}}
{{{(cosw)^2-(sinw)^2+3cosw-1=0}}}
Use FORMULA {{{(sinw)^2=1-(cosw)^2}}}
{{{(cosw)^2-(1-(cosw)^2)+3cosw-1=0}}}
{{{(cosw)^2-1+(cosw)^2+3cosw-1=0}}}
{{{2(cosw)^2+3cosw-2=0}}}
Let {{{cosw=t}}}, {{{-1<=t<=1}}}
{{{2t^2+3t-2=0}}}
 {{{t = (-3 +- sqrt( 3^2-4*2*(-2)))/(2*2) }}}
{{{t = (-3 +- sqrt( 25))/4 }}}  
{{{t = (-3 +5)/4 }}}  or {{{t = (-3 -5)/4 }}}  
{{{t = 1/2 }}}  or {{{t = -2 }}}>1
{{{t = 1/2 }}} , so {{{cosw=1/2}}}, 
Use FORMULA if {{{cosw=a}}}, then w=+-arccos(a)+360k, k is any integer
{{{cosw=1/2}}}
w=+-arccos(1/2)+360k 
w=+-60+360k, k is any integer