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If (costheta+cos2theta)^3=cos^3theta+cos...

If `(costheta+cos2theta)^3=cos^3theta+cos^3 2theta,` then the least positive value of `theta` is equal to `pi/6` (b) `pi/4` (c) `pi/3` (d) `pi/2`

Text Solution

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We have `(cos theta+ cos 2 theta)^(3)=cos^(3) theta+cos^(3) 2 theta`
i.e., `(a+b)^(3)=a^(3)+b^(3)`
`rArr ab(a+b)=0`
`rArr cos theta=0 or cos 2 theta=0 or cos theta+ cos 2 theta=0`
`rArr theta_(min)=pi/2 or theta_(min)=pi/4 or theta_(min)=pi/3`
`rArr theta_(min)=pi/4`
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