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The number of values of x in the interva...

The number of values of x in the interval `[0,3pi]` satisfying the equation` 2sin^(2)x+ 5 sin x -3=0` , is

A

6

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`2"sin"^(2) x + 5 "sin" x - 3 =0`
`rArr (2"sin"x-1)("sin" x + 3) =0`
`rArr 2"sin" x -1 =0 " " [because "sin" x + 3 ne 0]`
`rArr "sin"x = (1)/(2) rArr x = (pi)/(6), (5pi)/(6), (13pi)/(6), (17pi)/(6)`
Hence, there are four values of x.
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OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
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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. General solution of the equation, cos x cdot 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 ...

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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. Show that the equation , sec theta + "cosec" theta = c has two roots...

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  11. Show that the equation , sec theta + "cosec" theta = c has two roots...

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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 the value of cos(the...

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  14. If tan(pi cos theta )= cot (pi sin theta ) ,then cos^(2)(theta -pi/...

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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 solutions of the x+2tanx = pi/2 in [0.2pi] is

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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. Values of x between 0 and 2 pi which satisfy the equation sin x sqr...

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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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