witout-using-calculator-simpify-cos22-5-

Question Number 31549 by de best last updated on 10/Mar/18

w i t o u t u s i n g c a l c u l a t o r, s i m p i f y

c o s 22.5 °

Answered by $@ty@m last updated on 10/Mar/18

\cos 2 x = 2 \cos^{2} x - 1

\Rightarrow \cos x = \sqrt{\frac{1 + \cos 2 x}{2}}

∴ \cos 22 . 5^{o} = \sqrt{\frac{1 + \cos 45^{o}}{2}}

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

Commented by MJS last updated on 10/Mar/18

= \frac{\sqrt{2 + \sqrt{2}}}{2}

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