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Show that sqrt[2+sqrt[2+sqrt[2+2cos8thet...

Show that `sqrt[2+sqrt[2+sqrt[2+2cos8theta]]]=2costheta`

Text Solution

Verified by Experts

Here, we will use,
`cos2theta = 2cos^2theta - 1 => 1+cos 2theta = 2cos^2theta`
Now,
`L.H.S. = sqrt(2+sqrt(2+sqrt(2+2cos8theta)))`
`= sqrt(2+sqrt(2+sqrt(2(1+cos8theta))))`
`= sqrt(2+sqrt(2+sqrt(2(2cos^2 4theta))))`
`= sqrt(2+sqrt(2+2cos4theta))`
`= sqrt(2+sqrt(2(1+cos4theta)))`
...
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