Answer:
Option a. [tex]\frac{1}{2} \sqrt{2+\sqrt{3} }[/tex]
Step-by-step explanation:
In this question we have to find out the exact value of cos 15 by half angle identity.
As we know that [tex]cos(\frac{x}{2} ) = \sqrt{\frac{1+cosx}{2} }[/tex] is the half angle identity.
From half this identity we can write cos15 as
[tex]cos15 = cos\frac{30}{2}[/tex] = [tex]\sqrt{\frac{1+cos30}{2} }[/tex]
cos 15 = [tex]\sqrt{\frac{1+\frac{\sqrt{3} }{2} }{2} }[/tex]
= [tex]\sqrt{\frac{\frac{\sqrt{3}+2}{2} }{2} } = \sqrt{(\frac{\sqrt{3}+2 }{2})(\frac{1}{2})}[/tex]
= [tex]\sqrt{\frac{\sqrt{3}+2 }{4} } = [tex]\frac{1}{2} \sqrt{2+\sqrt{3} }[/tex]
So Option a.[tex]\frac{1}{2} \sqrt{2+\sqrt{3} }[/tex] is the right option.
