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

Mathematics

1 answer:

grandymaker [24]3 years ago

4 0

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

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

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

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