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Evaluate tan^(- 1)sqrt(3)-cot^(- 1)(-sqr...

Evaluate `tan^(- 1)sqrt(3)-cot^(- 1)(-sqrt(3))`

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Verified by Experts

The correct Answer is:
`(5pi)/6`
`tan^(-1)sqrt(3)=theta_(1) rArr tantheta_(1)=sqrt(3)=tanpi/3 rArr theta_(1)=pi/3`.
`cot^(-1)(-sqrt(3))=theta_(2) rArr cottheta_(2)=-sqrt(3)-cotpi/6=cot(pi-pi/6)=cot(5pi)/6`
`rArr theta_(2)=(5pi)/6`.
`therefore tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3))=(pi/3-(5pi)/6)`
`=-(3pi)/6=-pi/2`.
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RS AGGARWAL-INVERSE TRIGNOMETRIC FUNCTIONS -Exercise 4B
  1. tan^(-1)(-1)

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  2. sec^(-1)(-2)

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  3. The principal value of "cosec"^(-1)(-sqrt(2)) is

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  4. cot^(-1)(-1)

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  5. The principal value of tan^-1(-sqrt3) is

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  6. Find the principal value of sec^(-1)((-2)/(sqrt(3)))

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  7. "cosec"^(-1)(2)

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  8. प्रश्न संख्या 16 से 18में दिए प्रत्येक व्यंजन का मान ज्ञात कीजिए : ...

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  9. प्रश्न संख्या 16 से 18में दिए प्रत्येक व्यंजन का मान ज्ञात कीजिए : t...

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  10. cos^(-1)(cos""(7pi)/(6)) का मान बराबर है

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  11. निम्नलिखित के मान ज्ञात कीजिए : cos^(-1)(cos""(3pi)/(6))

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  12. निम्नलिखित के मान ज्ञात कीजिए : tan^(-1)(tan""(3pi)/(6))

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  13. Evaluate tan^(- 1)sqrt(3)-cot^(- 1)(-sqrt(3))

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  14. Sin[pi/3-sin^(-1)(-1/2)]

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  15. cot(tan^(- 1)x+cot^(- 1)x)

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  16. "cosec"(sin^(-1)x+cos^(-1)x)

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  17. sin(sec^(-1)x+"cosec"^(-1)x)

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  18. cos^-1 (1/2) + 2 sin^-1 (1/2).

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  19. Find the value of: tan^(-1)(1)+cos^(-1)(-1/2)+sin^(-1)(-1/2)

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  20. The value of sin^(-1)(sin'(3pi)/(5)) is "….."

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