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If sin^(-1)sqrt(x^2+2x + 1) + sec^(-1)sq...

If `sin^(-1)sqrt(x^2+2x + 1) + sec^(-1)sqrt(x^2 + 2x + 1) = pi/2; x!= 0,` then the value of `2sec^(-1)(x/2) + sin^(-1)(x/2)` is equal to

A

`-(3pi)/(2)`

B

`(3pi)/(2)`

C

`-(pi)/(2)`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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VMC MODULES ENGLISH-INVERSE TRIGONOMETRY-LEVEL-2
  1. It is given that A=(tan^(-1)x)^(3)+(cot^(-1)x)^(3) where x gt 0 and B=...

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  2. It is given that A=(tan^(-1)x)^(3)+(cot^(-1)x)^(3) where x gt 0 and B=...

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  3. If sin^(-1)sqrt(x^2+2x + 1) + sec^(-1)sqrt(x^2 + 2x + 1) = pi/2; x!= 0...

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  4. The value of a for which a x^2+sin^(-1)(x^2-2x+2)+cos^(-1)(x^2-2x+2)=1...

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  5. Find the sum of infinite series s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ...

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

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  7. Solution set of the inequality ( cot^(-1) x)^(2) - ( 5 cot^(-1) x) +...

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  8. Solve tan^(-1)x+sin^(-1)x=tan^(-1)2xdot

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  9. If sin^(-1)(x^2-4x+5)+cos^(-1)(y^2-2y+2)=pi/2 then find the value of x...

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  10. If x and y are positive integers such that tan^(-1)x+cot^(-1)y=tan^(-...

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  11. If cos^(-1)((7)/(|x|))+cos^(-1)((4sqrt(15))/(|x|))=(pi)/(2), then:

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  12. For the equation 2x=tan(2tan^(-1)a)+2 t a n(tan^(-1)a+tan^(-1)a^3) , w...

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  13. 2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),w h e r ex in R-{-1,1}, is equal to...

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  14. cos^(-1)x=tan^(-1)x then

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  15. Which of the following is/are correct?

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  16. Let x1,x2,x3,x4 be four non zero numbers satisfying the equation tan^...

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  17. The least value of n for which (n -2) x^(2) + 8 x + n + 4 gt sin^...

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  18. For x,y,z,t in R, if sin^(-1)x+cos^(-1)y+sec^(-1)z ge t^(2)-sqrt(2pi)*...

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  19. Let f(x)=(1)/(pi) (sin^(-1)x+cos^(-1)x+tan^(-1)x)+((x+1))/(x^(2)+2x+10...

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  20. The number of rational numbers in the domain of function y=sin^(-1)...

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