Question

Using the half angle formula, what is the exact value of Cos11pi/12?

Answer 1

Answer:

- $\frac{1}{2}$$\sqrt{2+\sqrt{3} }$

Step-by-step explanation:

Using the half angle formula

• cos($\frac{x}{2}$) = $\sqrt{\frac{1+cosx}{2} }$

here $\frac{x}{2}$ = $\frac{11\pi }{12}$, hence

x = $\frac{11\pi }{6}$

and cos ($\frac{11\pi }{6}$) = cos($\frac{\pi }{6}$) = $\frac{\sqrt{3} }{2}$

cos ($\frac{11\pi }{12}$)

= - $\sqrt{\frac{1+\frac{\sqrt{3} }{2} }{2} }$

= - $\sqrt{\frac{2+\sqrt{3} }{4} }$ = - $\frac{1}{2}$$\sqrt{2+\sqrt{3} }$