Compute-cos-12-

Question Number 111391 by Aina Samuel Temidayo last updated on 03/Sep/20

Compute \cos \frac{Π}{12}

Answered by bemath last updated on 03/Sep/20

\frac{π}{6} = 2 \times \frac{π}{12} \Rightarrow \cos \frac{π}{6} = \cos (2 . \frac{π}{12})

\frac{1}{2} \sqrt{3} = 2 \cos^{2} (\frac{π}{12}) - 1

\frac{\sqrt{3}}{2} + 1 = 2 \cos^{2} (\frac{π}{12}) \Rightarrow \cos \frac{π}{12} = \sqrt{\frac{2 + \sqrt{3}}{4}}

\cos \frac{π}{12} = \frac{1}{2} \sqrt{2 + \sqrt{3}}

Commented by bemath last updated on 03/Sep/20

haha . . why you think it not equivalent ?

Commented by bemath last updated on 03/Sep/20

Commented by bemath last updated on 03/Sep/20

look it

Commented by bobhans last updated on 03/Sep/20

creative sir . i like it

Answered by ajfour last updated on 03/Sep/20

\cos (\frac{π}{12}) = \cos (\frac{π}{3} - \frac{π}{4})

= \cos \frac{π}{3} \cos \frac{π}{4} + \sin \frac{π}{3} \sin \frac{π}{4}

= \frac{1}{2} \times \frac{1}{\sqrt{2}} + \frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{2}}

\cos \frac{π}{12} = \frac{\sqrt{2} + \sqrt{6}}{4} .

Commented by Aina Samuel Temidayo last updated on 03/Sep/20

Thanks .

Commented by bemath last updated on 03/Sep/20

\sqrt{{(\frac{\sqrt{2} + \sqrt{6}}{4})}^{2}} = \sqrt{\frac{8 + 2 \sqrt{12}}{16}} = \sqrt{\frac{8 + 4 \sqrt{3}}{16}}

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

clearr ? ? ?

Commented by Aina Samuel Temidayo last updated on 03/Sep/20

Yes . Thanks .