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If xge0 and theta=sin^(-1)x+cos^(-1)x-ta...

If `xge0` and `theta=sin^(-1)x+cos^(-1)x-tan^(-1)x`, then

A

`(pi)/(2) lt theta le (3pi)/(4)`

B

`0 le theta le (pi)/(4)`

C

`-(pi)/(4) le theta le 0`

D

`(pi)/(4) le theta le (pi)/(2)`

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Chapter Test
  1. The value of (alpha^(3))/(2) cosec^(2) ((1)/(2) tan^(-1) ((alpha)/(bet...

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  2. If a,b are positive quantitis and if a(1)=(a+b)/(2), b(1)=sqrt(a(1)b) ...

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  3. tan""(2pi)/(5)-tan""(pi)/(15)-sqrt3tan""(2pi)/(5)tan""(pi)/(15) is equ...

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  4. If a(1), a(2), a(3),...., a(n) is an A.P. with common difference d, th...

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  5. If x=sin(2tan^(- 1)2), y=sin(1/2tan^(- 1)(4/3)) , then -

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  6. Which of the following angles is greater? theta1=sin^(-1)+sin^(-1)1/3o...

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  7. The value of cos[1/2 cos^(-1){cos(sin^(-1)((sqrt63)/(8)))}] is

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  8. Solve for x: - tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

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  9. If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)...

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  10. The sum of the two angles cot^(-1) 3 and cosec^(-1) sqrt(5) is

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  11. Show that: cos(2tan^(-1)1/7)=sin(4^(-1)1/3)

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  12. The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x ...

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  13. cos{cos^(-1)(-1/7)+sin^(-1)(-1/7)} =

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  14. If cos^(-1)x + cos^(-1)y + cos^(-1)z = 3pi, then xy + yz +zx is equal ...

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  15. Evaluate: sin(1/2cos^(-1)4/5)

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  16. If xge0 and theta=sin^(-1)x+cos^(-1)x-tan^(-1)x, then

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  17. If tan^(-1)a+tan^(-1)b+tan^(-1)c=pi then prove tjhat a+b+c=abc

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  18. The value of cot("cosec"^(-1)(5)/(3)+"tan"^(-1)(2)/(3)) is :

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  19. Prove the following : sin^(-1)(4/5)+2\ tan^(-1)(1/3)=pi/2

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  20. The equation sin^-1x-cos^-1x=cos^-1(sqrt3/2) has

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