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Find the Value of \ sqrt(2+sqrt(2+2cos4t...

Find the Value of `\ sqrt(2+sqrt(2+2cos4theta))`

A

`2costheta`

B

`costheta`

C

`2cos(theta/2)`

D

`2cos(theta/4)`

Text Solution

Verified by Experts

The correct Answer is:
A
LHS= `sqrt(2+sqrt(2+sqrt(2(1+cos8theta))))`
`=sqrt(2+sqrt(2+sqrt2(2cos^(2)4theta)))`
`[because 1+cos 8theta=2cos^(2)(8theta)/(2)]`
`=sqrt(2+sqrt(2+sqrt(3(2cos^(2)4theta))))`
`=sqrt(2+sqrt(2+2cos4theta))`
`=sqrt(2+sqrt(2(1+cos4 theta)))`
`=sqrt(2+sqrt(2(2cos^(2)-2theta)))[because 1+cos 4 theta=2cos^(2)2theta]`
`=sqrt(2+2cos 2theta)`
`=sqrt(2(1+cos 2theta))`
`=sqrt(2(2cos^(2)theta))`
`=2cos theta=`RHS
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