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The principal value of "cosec"^(-1)(-sqr...

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

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The correct Answer is:
`(5pi)/4`
Range of `"cosec"^(-1)` is `[-pi2, pi/2]-{0}`.
`therefore "cosec"^(-sqrt(2))=0 rArr "cosec"theta=-sqrt(2)=-"cosec"pi/4="cosec"(pi+pi/4)="cosec"(5pi)/4`
`rArr theta=(5pi)/4`.
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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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