1.

Prove that: `-4le5costheta+3cos(theta+pi/3)+3 ge10`, for all values of `theta`.

Answer» We have, `5costheta+3costheta(theta+pi/3)=5costheta+3costhetacospi/3-3sinthetasinpi/3=13/2costheta-(3sqrt(3))/(2)sintheta`
Since `-sqrt((13/2)^(2)+(-3sqrt(3)/2)^(2)) le13/2 costheta-(3sqrt(3))/(2)sintheta le sqrt((13/2)^(2)+(-3sqrt(3))/(2)^(2))`
`rArr -7 le 13/2 costheta-(3sqrt(3))/(2)sintheta le7`
`rArr -7 le5costheta+3cos(theta+pi/3)le7` for all `theta`.
`rArr -7+3 le5costheta+3cos(theta+pi/3)+3 ge7 +3` for all `theta`
`rArr -4 le5 costheta+3cos(theta+pi/3)+3 le10` for all `theta`


Discussion

No Comment Found

Related InterviewSolutions