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If the equation kcosx-3sinx=k+1 has a so...

If the equation `kcosx-3sinx=k+1` has a solution for `x` then

A

`[4, oo)`

B

`[-4, 4]`

C

`(-oo, 4]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We know that
`|a "sin" x+ b"cos" x| le sqrt(a^(2) + b^(2))` for all x.
So, the given equation will be solvable, if
`|k + 1| le sqrt(k^(2) + 9) [because| k"cos" x - 3 "sin" x |le sqrt(k^(2) + 9) "and we have k cos" x -3 "sin" x = k + 1]`
`rArr (k + 1)^(2) le k^(2) + 9 rArr k le 4 rArr k in (-oo, 4]`
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OBJECTIVE RD SHARMA-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
  1. If the equation kcosx-3sinx=k+1 has a solution for x then

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  2. If |k|=5 and 0^(@) le theta le 360^(@) , then the number of different...

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  3. The number of all the possible triplets (a1,a2,a3) such that a1+a2cos(...

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  4. The number of all possible 5-tuples (a(1),a(2),a(3),a(4),a(5)) such th...

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  5. The general solution of the equation "cos" x"cos"6x = -1, is

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  6. The values of x satisfying the system of equation 2^("sin" x + "cos"...

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  7. The general solution of the equation "tan" 3x = "tan" 5x, is

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  8. The number of all possible ordered pairs (x, y) x, y in R satisfying t...

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  9. If the expression ([s in(x/2)+cos(x/2)-i t a n(x)])/([1+2is in(x/2)])...

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  10. If the equation "sec" theta + "cosec" theta =c has real roots between ...

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  11. If the equation "sec" theta + "cosec" theta =c has real roots between ...

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  12. If theta(1), theta(2), theta(3), theta(4) are roots of the equation "s...

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  13. If sin(pi cos theta) = cos(pi sin theta), then of the value cos(th...

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  14. If "tan" (pi "cos" theta) = "cot"(pi "sin" theta), then the value(s) ...

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  15. The general solution of "tan" ((pi)/(2)"sin" theta) ="cot"((pi)/(2)"co...

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  16. The most general value of theta which satisfy both the equation cos th...

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  17. The number of roots of the equation x +2"tan"x = (pi)/(2) in the inter...

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  18. If "sin" (pi "cot" theta) = "cos" (pi "tan" theta), "then cosec" 2 the...

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  19. The number of distinct roots of the equation A"sin"^(3) x + B"cos"^(3...

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  20. The values of x between 0 and 2pi which satisfy the equation sinxsqrt(...

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  21. If Cos20^0=k and Cosx=2k^2-1, then the possible values of x between 0^...

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