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Prove the following: 2+2+2+cos8x = 2 cosx - Mathematics and Statistics

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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