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If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) ...

If `sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab))`,
then prove that `b^(2)x^(2)+2xy sqrt(a^(2)b^(2)-c^(4)) +a^(2)y^(2)=c^(4)`

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MBD PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Solve: "tan"^(-1) 1/(2x+1) +"tan"^(-1) 1/(4x+1) = "tan"^(-1) 2/x^2

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

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

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

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

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

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

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

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

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

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

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  12. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  13. If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "co...

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  14. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

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  15. If "sin"^(-1)(x/a) + "sin"^(-1) (y/b)=alpha "prove that" x^2/a^2+(2xy)...

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  16. If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^...

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  17. Solve equation "tan"^(-1) (x-1)/(x+1) ="tan"^(-1) (2x-x)/(2x+1) = "tan...

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  18. Solve equation"tan"^(-1) 1/3 +"tan"^(-1) 1/5 +"tan"^(-1) 1/7 +"tan"^(-...

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  19. Solve equation "cos"^(-1)(x+1/2)+"cos"^(-1)x

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  20. Solve equation 3"tan"^(-1)1/((2+sqrt3)) - "tan"^(-1) 1/x ="tan"^(-1) 1...

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