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If r^2 =x^2 +y^2+z^2, "Prove that" "tan...

If `r^2 =x^2 +y^2+z^2, "Prove that" `
`"tan"^(-1) (yz)/(xr) ="tan"^(-1) (zx)/(yr) +"tan"^(-1) (xy)/(zr) =pi/2`

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MBD PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Solve:"sin"^(-1)2x+"sin"^(-1)x = pi/3.

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  17. Prove the Statement:"sin"^(-1)12/13-"sin"^(-1) 3/5 ="sin"^(-1) 33/65

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  18. Prove that : "cos"^(-1) ((b+a "cos"x)/(a+b "cos"x)) =2"tan"^(-1)(sqr...

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  19. Prove that : "tan"(pi/4 +1/2 "cos"^(-1) a/b) +"tan"(pi/4 -1/2 "cos"^(...

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  20. Prove that : "tan"^(-1)sqrt((xr)/(yz)) +"tan"^(-1) sqrt((yr)/(yx)) +"...

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