Respuesta :
we know that
Sine or Cosine of a Half Angle is giving by the formulas
[tex]\sin (\frac{x}{2})=+-\sqrt{\frac{(1-\cos x)}{2}}[/tex][tex]\cos (\frac{x}{2})=+-\sqrt{\frac{(1+\cos x)}{2}}[/tex]step 1
Find the value of Sin(30)
so
[tex]\sin (\frac{60}{2})=+-\sqrt{\frac{(1-\cos 60)}{2}}[/tex]substitute the given values
cos(60)=1/2
[tex]\sin (30)=+-\sqrt{\frac{(1-1/2)}{2}}=\pm\sqrt{\frac{1}{4}}=\frac{1}{2}[/tex]step 2
Find the value of Cos(30)
substitute the given values in the formula above
[tex]\cos (\frac{60}{2})=+-\sqrt{\frac{(1+\cos 60}{2}}[/tex][tex]\cos (30)=+-\sqrt{\frac{(1+1/2)}{2}}=\sqrt{\frac{3}{4}}=V3/2[/tex]step 3
Find the value of Cot(60)
REmember that
Cot=cos/sin
so
substitute
cot(60)=cos(60)/sin(60)
cot(60)=(1/2)/(V3/2)=V3/3
