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If Sin^(-1)(x)+Sin^(-1)(y)+Sin^(-1)(z) =...

If `Sin^(-1)(x)+Sin^(-1)(y)+Sin^(-1)(z) = pi`, prove that `xsqrt(1-x^(2)) + ysqrt(1-y^(2)) +zsqrt(1-z^(2)) = 2xyz`.

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The correct Answer is:
`2xyz = R.H.S`
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SRISIRI PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-SAQ (1D Star Q)
  1. P.T. Cos^(-1)((4)/(5))+Sin^(-1)((3)/(sqrt34))=Tan^(-1)((27)/(11)).

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  2. Find the value of sin(Cos^(-1)3/5+Cos^(-1)12/13)

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  3. Find cos(sin^(-1)3/5+sin^(-1)5/13)

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  4. Find the value of tan(Sin^(-1)3/5 + Cos^(-1) 5/(sqrt34)).

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  5. Find the value of tan(Cos^(-1)4/5 + Tan^(-1) 2/3)

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  6. Show that cot(Sin^-1sqrt(13/17))=sin(Tan^-1""2/3).

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

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  8. Prove that cos(2Tan^(-1)1/7) = sin(4Tan^(-1)1/3)

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

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  10. Show that Tan^(-1)3/4 + Tan^(-1)3/5 - Tan^(-1) 8/19 = (pi)/4.

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  11. Show that Tan^(-1) 1/7 + Tan^(-1) 1/8 = Cot^(-1) 201/43 + Cot^(-1) 18

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  12. Prove that Cot^(-1)9+"Cosec"^(-1) (sqrt(41))/4 = (pi)/4.

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  13. Prove that Sin^-1""4/5+Sin^-1""5/13+Sin^-1(16/65)=pi/2

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  14. Prove that sin^(-1)((4)/(5))+2 Tan^(-1)((1)/(3)) = (pi)/2.

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  15. Prove that sin[Cot^(-1) (2x)/(1-x^2)+Cos^(-1)((1-x^(2))/(1+x^(2)))]=1.

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  16. Show that tan[2 tan^(-1)((sqrt(5)-1)/(2))]=2

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  17. If Sin^(-1)x-Cos^(-1)x = (pi)/6 then find x.

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  18. If Tan^(-1)x+Tan^(-1)y + Tan^(-1)z = (pi)/2, then prove that xy + yz +...

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  19. If Sin^(-1)(x)+Sin^(-1)(y)+Sin^(-1)(z) = pi, prove that xsqrt(1-x^(2))...

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  20. If Cos^(-1)p+Cos^(-1)q+Cos^(-1)r = pi then, P.T. p^(2)+q^(2)+r^(2) = 2...

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