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If the expression ([s in(x/2)+cos(x/2)-...

If the expression `([s in(x/2)+cos(x/2)-i t a n(x)])/([1+2is in(x/2)])` is real, then the set of all possible values of `x` is.........

A

`2n pi + 2 "tan"^(-1)k, k in R, n in Z`

B

`2n pi + 2 "tan"^(-1)k," where " k in(0, 1), n in Z`

C

`2n pi + 2"tan"^(-1)k, "where" k in (1, 2), n in Z`

D

`2n pi + 2"tan"^(-1) k, k in (2, 3), n in Z`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
  1. The general solution of the equation "tan" 3x = "tan" 5x, is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. The general solution of the trigonometic equation "sin"x + "cos"x = 1...

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  17. The general solution of the equation sin^2thetasectheta+sqrt3 tantheta...

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  18. If x = X "cos" theta-Y "sin" theta, y = X "sin" theta + Y "cos" theta ...

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  19. The equation 3^("sin"2x + 2"cos"^(2)x) + 3^(1-"sin"2x +2"sin"^(2)x) = ...

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  20. The value of x , 0 le x le (pi)/2 which satisfy the equation 81^( si...

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