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Prove that cos [tan^(-1){(sin(cot^(-1)x}...

Prove that `cos [tan^(-1){(sin(cot^(-1)x}] =((x^(2)+1)/(x^(2)+2)) ^(1/2)`

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A DAS GUPTA-Inverse Circular Functions -Exercise
  1. Prove that cos [tan^(-1){(sin(cot^(-1)x}] =((x^(2)+1)/(x^(2)+2)) ^(1/2...

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  2. Prove that tan^ (-1)( 1/3) +tan^(-1)( 1/5) + tan^(-1) (1/7 )+tan^(-1) ...

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  3. Prove that 2cot^(-1)5+ cot^(-1)7 + 2cot^(-1)8 =pi/4

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  4. Prove that cos^(-1)(3/5) + cos^(-1) (12/13) + cos^(-1)( 63/65) =pi/2.

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  5. If sin^(-1)x/a +sin^(-1)y/b = sin^(-1) c^(2)/ab show that b^(2)x^(2) +...

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

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

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  8. If sin^(-1)x + sin^(-1)y = pi/2 prove that 2(x^(2) -x^(2)y^(2) + y^(2...

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  9. If tan^(-1)x+ tan^(-1)y + tan^(-1)z = pi, prove that x + y + z = xyz.

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  10. If cot^(-1)x + cot^(-1)y + cot^(-1)z = pi, prove that xy + yz + zx = ...

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  11. If sin^(-1)x + sin^(-1)y + sin^(-1)z =pi, prove that xsqrt(1 - x^(2))...

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  12. If in triangle ABC, C = 90^circ then prove that tan^(-1) (a/(c+b)) + ...

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  13. If in a triangle, two angles are tan^(-1)2 and tan^(-1)3 then prove t...

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  14. Solve tan^(-1)2x + tan^(-1)3x = pi/4

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

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  16. Solve: cos^(-1) ((x^(2)-1)/(x^(2)+1))+ tan^(-1) ((2x)/(x^(2)-1)) = (2p...

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  17. Solve: sin^(-1)6x + sin^(-1)6 sqrt3x =-pi/2.

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  18. Solve tan^(-1)2x + tan^(-1)3x = pi/4

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  19. The principal value of cos^(-1) (cos 7pi/6)= .

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  20. The principal value of tan^(-1)(-sqrt3) = .

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  21. find the value of sin(sin^(-1)a+cos^(-1)a)

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