The value of sqrt{2+sqrt{2(1+cos 4A)}} is equ | vedclass

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Question

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

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$2\cos A$

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(C) Given expression $= \sqrt{2+\sqrt{2(1+\cos 4A)}}$.Using the trigonometric identity $1+\cos 2	heta = 2\cos^2 	heta$,we have $1+\cos 4A = 2\cos^2 2A$.Substituting this into the expression,we get $\sqrt{2+\sqrt{2(2\cos^2 2A)}} = \sqrt{2+\sqrt{4\cos^2 2A}}$.This simplifies to $\sqrt{2+2\cos 2A}$.Again,using the identity $1+\cos 2	heta = 2\cos^2 	heta$,we have $2+2\cos 2A = 2(1+\cos 2A) = 2(2\cos^2 A) = 4\cos^2 A$.Therefore,the expression becomes $\sqrt{4\cos^2 A} = 2\cos A$.

The value of $\sqrt{2+\sqrt{2(1+\cos 4A)}}$ is equal to

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