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Question
Prove the following:
`sqrt(2 + sqrt(2 + sqrt(2 + 2cos8x)` = 2 cos x
Solution
L.H.S. = `sqrt(2 + sqrt(2 + sqrt(2 + 2 cos 8x)`
= `sqrt(2 + sqrt(2 + sqrt(2(1 + cos8x)`
= `sqrt(2 + sqrt(2 + sqrt(2 xx 2cos^2 4x)`
= `sqrt(2 + sqrt(2 + 2cos4x)`
= `sqrt(2 + sqrt(2(1 + cos 4x)`
= `sqrt(2 + sqrt(2 xx 2 cos^2 2x)`
= `sqrt(2 + 2cos 2x)`
= `sqrt(2(1 + cos 2x)`
= `sqrt(2 xx 2cos^2x)`
= 2 cos x
= R.H.S.
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