Question

Prove the following:

`sqrt(2 + sqrt(2 + sqrt(2 + 2cos8x)` = 2 cos x

Answer 1

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.