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Prove that : tan^(-1) a - tan^(-1) b = ...

Prove that : `tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(2))(1+b^(2))))]`

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NAGEEN PRAKASHAN ENGLISH-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 2a
  1. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

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  2. 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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  3. 4tan^(- 1)(1/5)=tan^(- 1)(1/70)-tan^(- 1)(1/99)+pi/4

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

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  5. tan[1/2 sin^(-1)((2a)/(1+a^2)) + 1/2 cos^(-1)((1-a^2)/(1+a^2))]=

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  6. Prove that : cos^(-1).(3)/(5)+ cos^(-1).(12)/(13) = sin^(-1)((63)/(65...

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  7. Prove that: sin^-1(3/5)-cos^-1(12/13)=sin^-1(16/65)

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  8. Prove that : cos^(-1).(4)/(5)+ tan ^(-1).(3)/(5) = tan^(-1) .(27)/(11)...

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  9. Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove tha...

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  10. If cos^(-1)(x/2)+cos^(-1)(y/3) = theta, prove that 9x^2- 12xycostheta+...

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  11. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

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  12. Solve : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x

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  13. Solve the equation for x : "sin"^(-1)(5)/(x)+"sin"^(-1)(12)/(x)=(pi...

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  14. Solve for x: - tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

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  15. The value of tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^...

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  16. Solve tan^-1(1/(1+2x))+tan^-1(1/(1+4x))=tan^-1(2/x^2)

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  17. If sin (picostheta) = cos (pisintheta) , then show that, theta = +-1/2...

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  18. If tan^(-1).(a+x)/(a) + tan ^(-1) ((a-x)/(a)) = (pi)/(6) then prove th...

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  19. If u= cot ^(-1) (sqrt(cos 2 theta)) -tan ^(-1)(sqrt(cos 2 theta)) , th...

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  20. Prove that : tan^(-1) a - tan^(-1) b = cos ^(-1) [(1+ab)/(sqrt((1+a^(...

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