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Prove that 4 tan^(-1) . 1/5 - tan^(-...

Prove that
` 4 tan^(-1) . 1/5 - tan^(-1) . 1/70 + tan^(-1) . 1/99 = pi/4`

A

`pi`

B

`pi//3`

C

`pi//4`

D

`pi//2`

Text Solution

Verified by Experts

The correct Answer is:
C
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ML KHANNA-INVERSE CIRCULAR FUNCTIONS -Problem Set (2)(MULTIPLE CHOICE QUESTIONS)
  1. Prove that tan^(-1). 1/2 + tan^(-1) . 1/5 + tan^(-1). 1/8 = pi/4

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  2. 2tan^(-1) ""1/5 + sec^(-1) ""(5sqrt2)/7 +2 tan^(-1)"1/8=

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  3. Prove that 4 tan^(-1) . 1/5 - tan^(-1) . 1/70 + tan^(-1) . 1/99 = ...

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  4. 4 tan^(-1)1/5-tan^(-1)1/239 is equal o

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  5. tan^(-1) (1/5) + tan^(-1) (1/7) + tan^(-1) (1/3) + tan^(-1) (1/8) = π/...

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  6. sin[1/2 cot^(-1)"(-3/4)] is equal to

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  7. Find the value of tan ( 1/2 cos ^(-1) . sqrt5/3)

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  8. tan^(-1)((1)/(4))+tan^(-1)((2)/(9)) is equal to :

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  9. cot[cos^(-1)"7/25]=

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  10. sin^(-1)(3/5)+tan^(-1)(1/7)=

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  11. If alpha=sin^(-1)"" 4/5+sin^(-1) ""1/3 and beta=cos^(-1) "" 4/5+cos^(-...

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  12. If cos^(-1)"" p/a+cos^(-1) ""q/b=alpha " then " p^2/a^2 - (2pq)/(ab) c...

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  13. If cos^(-1)x//2+cos^(-1) y//3=theta," prove that "9x^(2)-12xy cos thet...

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  14. If cos^(-1) x - cos^(-1). y/2= alpha ", then " 4x^(2) - 4xy cos alpha...

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  15. The value of cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt((1-sinx))-sqrt...

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  16. If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2)...

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  17. If xge1 , " then :" 2 tan^(-1)x+sin^(-1)((2x)/(1+x^(2)))=...

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  18. Evaluate : tan^(-1)1+tan^(-1)2+tan^(-1)3.

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  19. The value of sin^(-1){cot(sin^(-1)sqrt(((2-sqrt3)/4))+cos^(-1) (sqrt12...

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  20. The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+...

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