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The most general value of theta for whic...

The most general value of `theta` for which
`"sin" theta-"cos" theta = underset(x in R)("min")[1, x^(2)-4x+6]` are given by

A

`theta = n pi + (-1)^(n) (pi)/(4)-(pi)/(4), n in Z`

B

`theta = n pi + (-1)^(n) (pi)/(4) + (pi)/(4), n in Z`

C

`theta = 2 n pi + (pi)/(4), n in Z`

D

none of these

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
  1. Let alpha, beta be any two positive values of x for which 2"cos"x, |"c...

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  2. If max {5 sin theta + 3 sin ( theta - alpha )}=7 , then the set of pos...

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  3. The most general value of theta for which "sin" theta-"cos" theta = ...

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  4. The number of points of intersection of two curves y=2sinxa n dy=5x^2+...

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  5. Let 2 sin^(2)x + 3 sin x -2 gt 0 and x^(2)-x -2 lt 0 ( x is measured ...

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  6. The largest positive solution of 1+"sin"^(4) x = "cos"^(2) 3x " in " [...

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  7. The set of values of x in (-pi, pi) satisfying the inequation |4"sin" ...

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  8. If theta in [0, 5pi] and r in R such that 2 sin theta = r^(4) -2r^(2) ...

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  9. If rsintheta=3, r=4(1+sintheta) where 0<=theta<=2pi then theta e...

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  10. The solution set of the inequation "log"(1//2) "sin" x gt "log"(1//...

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  11. If the equation "sin" theta ("sin" theta + 2 "cos" theta) = a has a re...

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  12. The equation "sin"^(4) theta + "cos"^(4) theta = a has a real solution...

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  13. If 32"tan"^(8)theta" = 2"cos"^(2) alpha- 3"cos" alpha " and "3"cos" 2 ...

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  14. The general value of theta satisfying tantheta tan(120^@-theta) tan(12...

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  15. The solution of the equation "log"("cos"x) "sin" x + "log"("sin"x) "...

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  16. The number of solutions of the equation tanx+secx=2cosx lying in the i...

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  17. One root of the equation "cos" theta-theta + (1)/(2) = 0 lies in the i...

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  18. If "sin" (pi "cos" theta) = "cos" (pi "sin" theta), then which one fo ...

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  19. If "2sec" (2alpha) = "tan" beta + "cot"beta, then one of the value of ...

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  20. The values of k for which the equation sin^4 x+cos^4 x+sin2x+k=0 posse...

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