3 years ago

I really need help please help me

Mathematics

1 answer:

Bezzdna [24]3 years ago

7 0

Answer:

it's c

Step-by-step explanation:

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Read 2 more answers

How do you solve cos(pi/24) using Half-Angle formulas, and leaving in simplified form?

adoni [48]

$\cos \frac{\theta}{2}=\sqrt{\frac{1+\cos \theta}{2}}
\\
\\ \cos{\frac{\pi}{24}}=\cos{\frac{\frac{\pi}{12}}{2}}=\sqrt{\frac{1+\cos \frac{\pi}{12}}{2}}= \sqrt{ \frac{1}{2}+ \frac{\cos \frac{\pi}{12}}{2} } 
\\
\\ \cos{\frac{\pi}{12}}=\cos{\frac{\frac{\pi}{6}}{2}}=\sqrt{\frac{1+\cos \frac{\pi}{6}}{2}}= \sqrt{ \frac{1}{2}+ \frac{ \frac{ \sqrt{3} }{2} }{2} } =\sqrt{ \frac{2}{4}+ \frac{ \sqrt{3} }{4} } = \sqrt{\frac{ 2+\sqrt{3} }{4} } = 
\\
\\ =\frac{ \sqrt{2+\sqrt{3}} }{2} 
$

$\cos{\frac{\pi}{24}}= \sqrt{ \frac{1}{2}+ \frac{\cos \frac{\pi}{12}}{2} } = \sqrt{ \frac{1}{2}+ \frac{\frac{ \sqrt{2+\sqrt{3}} }{2}}{2} } = \sqrt{ \frac{2}{4}+ \frac{ \sqrt{2+\sqrt{3}} }{4}} } =\sqrt{ \frac{ 2+\sqrt{2+\sqrt{3}} }{4}} } 
\\
\\\cos{\frac{\pi}{24}}=\frac{\sqrt{2+\sqrt{2+\sqrt{3}}}} {2}$

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3 years ago