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The number of solutions of the equation ...

The number of solutions of the equation `2 "tan" x + x = (12 pi)/(5) " in the interval " [0, 2 pi]`, is

A

1

B

2

C

3

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`2 "tan" x + x = (12pi)/(5) rArr "tan"x = (6pi)/(5) - (x)/(2)`

It is evident from the graphs of `y = "tan "x "and " y = -(x)/(2) + (6pi)/(5)` that
they intersect at exactly two points in `[0, 2 pi]`.
Hence, the given equation has just two solutions.
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OBJECTIVE RD SHARMA-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
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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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