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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-TRIGONOMETRIC FUNCTIONS -SINGLE CORRECT ANSWER TYPE
  1. Find the values of x for which 3costheta=x^2-8x+19 holds good.

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  2. The circular wire of diameter 10 cm is cut and placed along the circum...

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  3. sintheta/(1-cottheta)+costheta/(1-tantheta)= (a)theta (b)1 (c)costh...

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  4. If theta in (pi//4, pi//2) and sum(n=1)^(oo)(1)/(tan^(n)theta)=sin the...

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  8. If (sin^(2)x-2cos^(2)x+1)/(sin^(2)x+2cos^(2)x-1)=4, then the value of ...

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  9. If sintheta,tantheta,costheta are in G.P. then 4sin^2theta-3sin^4theta...

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  10. If tantheta-cottheta=aandsintheta+costheta=b(b^2-1)^2(a^2+4) is equal...

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  11. The least value of 18 sin^(2)theta+2 cosec^(2)theta-3 is

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  17. Which of the following is true ?

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  18. If the angle A of a triangle ABC is given by the equation 5 cos A + 3 ...

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  19. Which of the following is greatest ?

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  21. Which of the following is not correct ?

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