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The values of x satisfying "tan"^(-1)...

The values of x satisfying
`"tan"^(-1) (x+3) -"tan"^(-1) (x-3) = "sin"^(-1)((3)/(5))` are

A

`+-4`

B

0, 4

C

`-4, 0`

D

4, 5

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`"tan"^(-1) (x+3) -"tan"^(-1) (x-3) = "sin"^(-1)(3)/(5)`
`rArr "tan"^(-1){((x+3) - (x-3))/(1+(x^(2)-9))} = "tan"^(-1) (3)/(4)`
`rArr -(6)/(x^(2)-8) = (3)/(4) rArr x^(2) = 16 rArr x = +-4`
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OBJECTIVE RD SHARMA-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
  1. The values of x satisfying "tan"^(-1) (x+3) -"tan"^(-1) (x-3) = "si...

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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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