Sum
Prove the following:
`sqrt(2 + sqrt(2 + sqrt(2 + cos8x)` = 2 cosx
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Solution
L.H.S. = `sqrt(2 + sqrt(2 + sqrt(2 + cos8x)`
= `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 2cos^2 2x)`
= `sqrt(2 + 2cos 2x)`
= `sqrt(2(1 + cos 2x)`
= `sqrt(2 xx 2cos^2x)`
= 2 cos x
= R.H.S.
[Note : Question is modified.]
Concept: Trigonometric Functions of Double Angles
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