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Prove that cos^(-1)(x)+ cos^(-1){(x)/(2)...

Prove that `cos^(-1)(x)+ cos^(-1){(x)/(2)+sqrt(3-3x^(2))/(2)}=(pi)/(3)`.

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SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  2. Solve: tan^(-1)x+2cot^(-1)x=(2pi)/3

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  3. Prove that cos^(-1)(x)+ cos^(-1){(x)/(2)+sqrt(3-3x^(2))/(2)}=(pi)/(3).

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  4. Prove that: cot^(-1)7+cot^(-1)18=cot^(-1)5.

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  5. Prove that: sin^(-1)(3/5)+sin^(-1)(8/17)=tan^(-1)(77/36).

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  6. Prove that sin^(-1)((4)/(5)) +sin^(-1)((5)/(13)) +sin^(-1)((16)/(65)...

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  7. Prove that "tan"^(-1)(1/4)+"tan"^(-1)(2/9)=1/2"tan"^(-1)(4/3).

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

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

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  10. If "sin"^(-1)(1-x)(1)-2"sin"^(-1)x=pi/(2), then find the value of x.

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

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  12. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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

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  14. Solve for x tan^(-1)(x+2)+tan^(-1)(x-2)=tan^(-1)(8/79),x>0.

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  15. Prove that: tan^(-1)(3/4)+tan^(-1)(3/5)-tan^(-1)(8/19)=pi/4

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  16. cos^(-1)x+cos^(-1)y+cos^(-1)z=pi ,then prove that, x^2+y^2+z^2+xyz=1

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

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

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  19. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

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

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