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Let f(theta)=sintheta(sintheta+sin3theta...

Let `f(theta)=sintheta(sintheta+sin3theta)dot` Then `f(theta)i s` `geq0on l yw h e nthetageq0` (b) `lt=0fora l lr e a ltheta` `geq0fora l lr e a ltheta` (d) `lt=0on l yw h e nthetalt=0`

A

`ge0"only when"thetage0`

B

`lt0"for all real"theta`

C

`ge0"for all real"0`

D

`le0"only when"le0`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`f(theta)=sintheta(sintheta+sin3 theta)`
`=2sinthetasinthetacostheta`
`=2sinthetasin2 thetacostheta`
`=sin^(2)2 thetage"for all real"theta.`
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