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Find the values of x for which 3costheta...

Find the values of x for which `3costheta=x^2-8x+19` holds good.

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`3cos theta=x^2-8x+19`
`rArr3costheta=(x-4)^2+3`
Now, `L.H.S. =3costhetale3`
or L.H.S. has greatest value 3
But `R.H.S.(x-4)^2+3ge3`
or R.H.S.has least value 3
Hence, L.H.S.=R.H.S. when `3costheta=(x-4)^2+3=3`
`rArr costheta=1" and "x-4=0`
`rArr theta=2n pi " and " x=4," where "in Z`.
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CENGAGE ENGLISH-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
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