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

If `Sin^(-1)x + Sin^(-1)y + Sin^(-1)z = pi`, then prove that `x^(4) + y^(4) + z^(4) + 4x^(2)y^(2)z^(2) = 2(x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2))`.

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The correct Answer is:
`2x^(2) y^(2) + 2y^(2) z^(2) + 2z^(2) x^(2)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-INVERSE TRIGONOMETRIC FUNCTIONS-SOLVED PROBLEMS
  1. Find the values of the following: sin^(2)("Tan"^(-1)3/4)

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  2. Find the values of the following: sin((pi)/2-Sin^(-1)(-4/5))

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  3. Find the value of the following: cos(Cos^(-1)(-2/3)-Sin^(-1)(2/3))

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  4. Show that Sec^(2)(cot^(-1)3)+(Cosec^(2)(tan^(-1)2))=85/36

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  5. Find the value of the following cot^(-1)(1/2)+cot^(-1)(1/3)

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  6. Prove that Sin^(-1)(4/5)+Sin^(-1) 7/25 = Sin^(-1) 117/125.

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  7. If x in (-1,1) prove that 2Tan^(-1)x="Tan"^(-1)(2x)/(1-x^(2))

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  8. sin^(-1)(4/5)+sin^(-1)(5/13)+sin^(-1)(16/65)=

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

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

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  11. Find the value of tan(2"Tan"^(-1)(1/5)-(pi)/4)

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

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

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  14. If Sin^(-1)x + Sin^(-1)y + Sin^(-1)z = pi, then prove that x^(4) + y^(...

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  15. If "Cos"^(-1)P/a+"Cos"^(-1)q/b=alpha, then prove that (p^(2))/(a^(2)...

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  16. Solve : sin^(-1) (5/x) + sin^(-1) (12/x) = (pi)/2

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  17. Solve Sin^(1)"" (3x)/5 + Sin^(-1)""(4x)/5 = Sin^(-1)x

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  18. Solve Sin^(-1)x +Sin^(-1)2x = (pi)/3.

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  19. Sin[2Cos^(-1){Cot(2tan^(-1)x)}]=0 Find x

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  20. Prove that cos[Tan^(-1){sin(Cot^(-1)x)}] = sqrt((x^(2)+1)/(x^(2)+2))

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