Question

please answer fast of question 18please

Answer 1

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Answer 2

Solution :

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Given :

Cos A = $\sqrt{ \frac{1 + Cos 2A}{2} }$

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To find :

Cos 30° using Cos 60°

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We know that,


Cos 60° = $\frac{1}{2}$

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Hence,

If A = 30°

Then,

⇒ Cos A = $\sqrt{ \frac{1 + Cos 2A}{2} }$


⇒ Cos 30° = $\sqrt{ \frac{1 + Cos 2(30)}{2} }$

⇒ Cos 30° = $\sqrt{ \frac{1 + Cos 60}{2} }$

⇒ Cos 30° = $\sqrt{ \frac{1 +  \frac{1}{2} }{2} }$

⇒ Cos 30° = $\sqrt{ \frac{ \frac{2+1}{2} }{2} }$

⇒ Cos 30° = $\sqrt{ \frac{ \frac{3}{2} }{2} }$

⇒ Cos 30° = $\sqrt{ (\frac{3}{2})( \frac{1}{2} ) }$

⇒ Cos 30° = $\sqrt{ \frac{3}{4} }$

⇒ Cos 30° = $\frac{ \sqrt{3} }{2}$

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                                    Hope it Helps !!