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Prove that : tan^(-1)((sqrt(1+x^(2))+s...

Prove that :
`tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2)`

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CBSE COMPLEMENTARY MATERIAL-INVERSE TRIGONOMETRIC FUNCTIONS-4 MARK QUESTIONS
  1. Prove that : tan^(-1)((cosx)/(1-sinx))-cot^(-1)(sqrt((1+cosx)/(1-cosx)...

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  2. Prove that tan^(-1)((x)/(sqrt(a^(2)-x^(2))))="sin"^(-1)(x)/(a)=cos^(-1...

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  3. Prove that : tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-s...

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  4. Solve : cot^(-1)2x+cot^(-1)3x=(pi)/(4)

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  5. Prove that: tan[(pi)/(4)+(1)/(2) tan^(-1)((a)/(b))]+tan[(pi)/(4)-(1)/...

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  6. Solve for x, cos^(-1)((x^(2)-1)/(x^(2)+1))+tan^(-1)((-2x)/(1-x^(2)))=(...

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  7. Prove that ta n^-1 1/3 + ta n ^-1 1/5 + ta n ^-1 1/7 + ta n ^-1 1/8 =...

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  8. tan(cos^(- 1)x)=sin(tan^(- 1)2)

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  9. If y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")), prove that siny=ta...

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  10. cot{tan^(- 1)x+tan^(- 1)(1/x)}+cos^(- 1)(1-2x^2)+cos^(- 1)(2x^2-1)=pi,...

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  11. Prove that tan^(-1)((a-b)/(1+ab))+ tan^(-1)((b-c)/(1+bc))+tan^(-1)((c-...

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  12. Q. if tan^-1 a+tan^-1 b+tan^-1 c=pi, then prove that a+b+c=abc.

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  13. If cos^(-1)x+cos^(-1)y+cos^(-1)=pi,p rov et h a tx^2+y^2+z^2+2x y z=1.

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  14. if tan^-1(1/(1+1*2))+tan^-1(1/(1+2*3))+.............+tan^-1(1/(1+n*(n+...

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  15. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

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  16. If"sin"{cot^(-1)(x+1)}="cos"(tan^(-1)x), then find xdot

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  17. Solve the equation sin^(-1)y x+sin^(-1)6sqrt(3)x=(-pi)/2dot

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  18. If sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x then x equals

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

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  20. Solve the following for x sin^(-1)((x)/(2))+cos^(-1)x=(pi)/(6)

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