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Prove the sin^2(sin^(-1) x+sin^(-1) y+s...

Prove the ` sin^2(sin^(-1) x+sin^(-1) y+sin^(-1)z)`
`=cos^2 (cos^(-1)x +cos^(-1) y+cos^(-1) z)`

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MBD PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Prove the "tan"^(-1) 1/(x+y) + "tan"^(-1) y/(x^2=xy+1) ="tan"^(-1)1/x

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  2. Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)sqrt((p-x)/(p-q))="co...

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  3. Prove the sin^2(sin^(-1) x+sin^(-1) y+sin^(-1)z) =cos^2 (cos^(-1)x +c...

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  4. Prove the "tan"("tan"^(-1)x +"tan"^(-1) y + "tan"^(-1)z)="cot"("cot"^-...

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  5. If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi, show that xsqrt(1-x^(2))+ys...

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  6. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

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  7. If tan^(-1)x +tan^(-1) y +tan^(-1) z=pi/2. Show that xy+yz+zx =1.

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  8. If r^2 =x^2 +y^2+z^2, "Prove that" "tan"^(-1) (yz)/(xr) ="tan"^(-1) (...

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  9. In a triangle ABC "if" m/A =90^@, "prove that "tan"^(-1) b/(a+b) +"ta...

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  10. Solve:cos(2"sin"^(-1)x)= 1/9

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  11. Solve: 2sin^(-1) x +sin^(-1) (1-x)= pi/2

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

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  13. Solve: "cos"^(-1) x +"sin"^(-1) x/2= pi/6

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  14. Solve: "tan"^(-1)(x-2)/(x-2) + "tan"^(-1) (x+1)/(x+2)=pi/4

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  15. Solve: "tan"^(-1) 1/(2x+1) +"tan"^(-1) 1/(4x+1) = "tan"^(-1) 2/x^2

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  16. Solve: 3 "sin"^(-1) (2x)/(1+x^2) -4"cos"^(-1) (1-x^2)/(1+x^2) +2 "tan"...

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  17. Solve:"cot"^(-1) 1/(x-1) + "cot"^(-1) 1/x +"cot"^(-1) 1/(x+1) = "cot"^...

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  18. Solve: "cot"^(-1)(1-x^2)/(2x) = "cosec"^(-1)(1+a^2)/(2a) -"sec"^-1 (1+...

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  19. Solve: "sin"^(-1)((2a)/(1+a^2) )+"sin"^(-1)((2b)/(1+b^2)) = 2"tan"^(-1...

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  20. Solve: "sin"^(-1) x - "cos"^(-1)x="cos"^(-1) sqrt3/2

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