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Express "sin"^(-1)[(sqrt(1+x)+sqrt(1-x))...

Express `"sin"^(-1)[(sqrt(1+x)+sqrt(1-x))/(2)],0ltxlt1` in the simplest form.

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The correct Answer is:
`pi/(4)+1/(2)"cos"^(-1)x`
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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Part II (QUESTIONS FOR PRACTICE)
  1. If "tan"^(-1)x+"tan"^(-1)y=pi/4,xylt1, then write the value of x+y+x...

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

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  3. Show that tan((1)/(2)"sin"^(-1)(3)/(4))=(4-sqrt(7))/(3).

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  4. Solve for x, cos (2sin^(-1)x)=(1)/(9), x gt 0.

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  5. If "sin"^(-1)(1-x)(1)-2"sin"^(-1)x=pi/(2), then find the value of x.

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  6. If "tan"^(-1)((x-2)/(x-4))+"tan"^(-1)((x+2)/(x+4))=pi/(4), then find t...

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  7. Solve for x, "tan"^(-1)((2x)/(1-x^(2)))+""cot"^(-1)((1-x^(2))/(2x))=...

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  8. Find the value of expression "sin"(2"tan"^(-1)1/(3))+"cos"("tan"^(-1...

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  9. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  10. If "tan"^(-1)a+"tan"^(-1)b+"tan"^(-1)c=pi, then prove that a+b+c=abc.

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  11. Solve for x, "tan"^(-1)x+2"cot"^(-1)x=(2pi)/(6).

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  12. Prove that (9pi)/(8) -(9)/(4) sin^(-1)((1)/(3)) =(9)/(4) sin^(-1)((2sq...

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  13. Prove that following cot^(-1)((xy+1)/(x-y)) +cot^(-1)((yz+1)/(y-z))+...

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  14. If "cos"^(-1)alpha+"cos"^(-1)beta+"cos"^(-1)gamma=3pi, then find alpha...

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  15. Prove that "tan"^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-s...

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  16. Prove that 2"tan"^(-1)(1/(5))+"sec"^(-1)((5sqrt(2))/(7))+2"tan"^(-1)(1...

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  17. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  18. Solve for x, "tan"^(-1)(x+1)+"tan"^(-1)(x-1)="tan"^(-1)8/(31)[0ltxlt1]...

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  19. Express "sin"^(-1)[(sqrt(1+x)+sqrt(1-x))/(2)],0ltxlt1 in the simplest ...

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  20. If (tan^(-1)x)^(2) +(cot^(-1)x)^(2) =(5pi^(2))/(8), then find x.

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