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If sin ^(-1) x=(1)/(3), then evaluate ...

If ` sin ^(-1) x=(1)/(3)`, then evaluate ` sin ^(-1) (2xsqrt(1-x^(2)))`

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Verified by Experts

The correct Answer is:
`(2)/(3)`
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NAGEEN PRAKASHAN-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 2a
  1. If tan ^(-1).(3)/(4)=x, the find the value of sex x.

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  2. (i) Evaluate : sec (cos^(-1).(1)/(2)) (ii) slove the equations si...

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  3. If sin ^(-1) x=(1)/(3), then evaluate sin ^(-1) (2xsqrt(1-x^(2)))

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  4. prove that: 2 tan ^(-1)x =(1)/(3) tan^(-1).(1)/( 7) = (pi)/(4)

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  5. Prove that : tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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  6. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=[pi/4m/n >-1(-3pi)/4m/n...

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  7. Prove that : tan^(-1).(x)/(x+1)- tan ^(-1) (2x +1) = (3pi)/(4)

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

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  9. Prove that : cot^(-1) 3 + cot^(-1).(3)/(4) = cot^(-1) .(1)/(3)

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  10. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

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  11. If cos^(-1)x+cos^(-1)y+cos^(-1)=pi,p rov et h a tx^2+y^2+z^2+2x y z=1.

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  12. 4tan^(- 1)(1/5)=tan^(- 1)(1/70)+tan^(- 1)(1/99)+pi/4

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  13. Prove that : cos ^(-1) ((1- a^(2))/(1+a)) + cos ^(-1)((1-b^(2))/(1+b...

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  14. tan[1/2 sin^(-1)((2a)/(1+a^2)) + 1/2 cos^(-1)((1-a^2)/(1+a^2))]=

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  15. Prove that : cos^(-1).(3)/(5)+ cos^(-1).(12)/(13) = sin^(-1)((12)/(5)...

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  16. Prove that: sin^-1(3/5)-cos^-1(12/13)=sin^-1(16/65)

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  17. If cos^(-1)(x/2)+cos^(-1)(y/3) = theta, prove that 9x^2- 12xycostheta+...

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  18. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

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  19. Solve : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x

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  20. (i) Solve : 4 sin ^(-1) .(5)/(x) + sin ^(-1).(12)/(x)=(pi)/(2) (ii)...

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