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

Prove that
`2 tan^(-1) . 1/7 +tan^(-1) . 1/3 = tan^(-1) . 9/13`

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Prove that tan^(-1). 1/2 +tan^(-1). 2/11 = tan^(-1) . 3/4

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

Prove the following 2 tan^(-1). 1/2 +tan^(-1) . 1/7 = tan^(-1). 31/17

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MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-EXERCISE 2 (b) (Short Answer Type Questions)
  1. Prove that 2tan^(-1) . 1/5 +tan^(-1). 1/4 = tan^(-1) . 32/43

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  2. Prove that 2 tan^(-1) . 1/5 +tan^(-1) . 1/6 = tan^(-1). 9/13

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  3. Prove that 2 tan^(-1) . 1/7 +tan^(-1) . 1/3 = tan^(-1) . 9/13

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  4. Prove that tan^(-1). 1/2 +tan^(-1). 1/5 = 1/2 cos^(-1). 16/65

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  5. Prove that: tan^-1(1/4)+tan^-1(2/9)=1/2 cos^-1(3/5).

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

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

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

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  9. Prove that cos^(-1).(4)/(5) + cos^(-1).(12)/(13) = cos^(-1).(33)/(65)

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  10. cos^(-1)((12)/(13))+sin^(-1)((3)/(5))=

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

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  12. Prove that sin^(-1) . 8/17 +sin^(-1) . 3/5 = sin^(-1) . 77/85

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  13. Prove that sin^(-1) . 8/17 +cos^(-1). 4/5 = cot^(-1) ((36)/77)

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  14. Prove that sin^(-1) . 8/17 +cos^(-1) . 4/5 = cos^(-1). 36/85

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  15. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

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  16. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

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  17. Prove that sin^(-1). 3/5 +cos^(-1) . 12/13 = sin^(-1). 56/65

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  18. Prove that sin^(-1) . 3/5 - sin ^(-1) . 8/17 = cos^(-1) . 84/85

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  19. cos^-1(4/5)+tan^-1(3/5)=tan^-1(27/11)

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  20. Prove that : tan^(-1)(63)/(16)=sin^(-1)5/(13)+cos^(-1)3/5

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