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If tan (cot x) = cot (tan x), prove that...

If `tan (cot x) = cot (tan x)`, prove that : `sin 2x = 4/((2n+1) pi)`

A

`"sin" 2x = (2)/((2n + 1)pi), n in Z`

B

`"sin" x = (4)/((2n + 1)pi), n in Z`

C

`"sin" 2x = (4)/((2n + 1)pi), n in Z`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`"tan " ("cot" x) = "cot" ("tan"x)`
`rArr "tan"("cot"x) = "tan" ((pi)/(2) - "tan"x), n in Z`
`rArr "cot" x = n pi + ((pi)/(2)-"tan"x), n in Z`
`rArr "cot"x + "tan" x = (2n + 1) (pi)/(2)`
`rArr (2)/("sin"2x) = (2n + 1) (pi)/(2) rArr "sin" 2x = (4)/((2n + 1)pi), n in Z`
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OBJECTIVE RD SHARMA-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Chapter Test
  1. If tan (cot x) = cot (tan x), prove that : sin 2x = 4/((2n+1) pi)

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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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