sqrt {2 + sqrt {2 + 2cos 4theta } } = | vedclass

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Question

(A) Given expression: $\sqrt {2 + \sqrt {2 + 2\cos 4	heta } }$Using the trigonometric identity $1 + \cos 2A = 2\cos^2 A$,we have $2 + 2\cos 4	heta =

Vedclass · Accepted Answer

$2\cos 	heta $

Vedclass · Answer

(A) Given expression: $\sqrt {2 + \sqrt {2 + 2\cos 4	heta } }$Using the trigonometric identity $1 + \cos 2A = 2\cos^2 A$,we have $2 + 2\cos 4	heta = 2(1 + \cos 4	heta) = 2(2\cos^2 2	heta) = 4\cos^2 2	heta$.Substituting this into the inner square root:$\sqrt {2 + \sqrt {4\cos^2 2	heta } } = \sqrt {2 + 2\cos 2	heta }$Again,using the identity $1 + \cos 2A = 2\cos^2 A$,we have $2 + 2\cos 2	heta = 2(1 + \cos 2	heta) = 2(2\cos^2 	heta) = 4\cos^2 	heta$.Taking the square root:$\sqrt {4\cos^2 	heta } = 2\cos 	heta$.Thus,the correct option is $A$.

$\sqrt {2 + \sqrt {2 + 2\cos 4\theta } } = $

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