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The value of expression tan^(- 1)((sqrt(...

The value of expression `tan^(- 1)((sqrt(2))/2)+sin^(- 1)((sqrt(5))/5)-cos^(- 1)((sqrt(10))/10)`

A

`cot^(-1) ((1+sqrt2)/(1-sqrt2))`

B

`cot^(-1) ((sqrt2 + 1)/(sqrt2-1))`

C

`- pi + cot^(-1) ((1+sqrt2)/(1 - sqrt2))`

D

`pi - cot^(-1) ((1-sqrt2)/(1 + sqrt2))`

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single Option Correct Type Questions)
  1. For any real number x ge 1, the expression sec^(2)x ( tan^(-1)x) - ...

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  2. Let f : R to [0, pi/2) be defined by f ( x) = tan^(-1) ( x^(2) + x +...

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  3. The value of expression tan^(- 1)((sqrt(2))/2)+sin^(- 1)((sqrt(5))/5)-...

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  4. The value of sec ( 2 cot^(-1) 2 + cos^(-1) . 3/5) is equal to

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  5. Which one of the following statement is meaningless ?

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  6. The value of sec(sin^-1(sin((-50pi)/9))+cos^-1(cos(31pi)/9))

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  7. The number k is such that tan { arc tan (2) + arc tan (20 k) } = k. ...

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  8. The value of Sigma( r =1)^( infty) tan^(-1) ( 1/( r^(2) - 5r + 7)) ,...

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  9. If x = tan^(-1) 1 - cos^(-1) ( - 1/2) + sin^(-1) 1/2 , y = cos (1/2 c...

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  10. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cotA)+tan^(-1)(cot^3A)=0

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  11. Prove that : tan^-1(1/2) + tan^-1(1/5) + tan^-1(1/8) = pi/4

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  12. Number of solutions (s) of the equations cos^(-1) ( 1-x) - 2 cos^(-...

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  13. There exists a positive real number of x satisfying "cos"(tan^(-1)x)=x...

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  14. The range of values of p for which the equation sin cos^(-1) (cos (tan...

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  15. Number of solutions of the equation log(10) ( sqrt(5 cos^(-1) x -1 ...

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  16. Solve sin^(-1) x+ cos^(-1) x = sin^(-1) (3x -2)

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  17. The set of values of x, satisfying the equation tan^2(sin^-1x) > 1 is ...

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  18. The solution set of equation sin^(-1) sqrt(1-x^2) + cos^(-1) x = cot^(...

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  19. The value of the angle tan^(-1) ( tan 65^(@) - 2 tan 40^(@)) in degree...

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  20. Prove that cotx - 2cot2x = tanx

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