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If tan^(-1)(sqrt(3))+cot^(-1)x=pi/2 , fi...

If `tan^(-1)(sqrt(3))+cot^(-1)x=pi/2` , find `xdot`

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Given,
`tan^(−1sqrt(3)​+cot^(−1)x=π/2​`
`⇒π/3​+cot^(−1)x=π/2​`
`⇒cot^(−1)x=π/2​−π/3​=π/6​`
`⇒x=cot(π/6)​=sqrt(3) `​
...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Show that sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x

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

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  3. If tan^(-1)(sqrt(3))+cot^(-1)x=pi/2 , find xdot

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  4. If sin^(-1)(1/3)+cos^(-1)x=pi/2,t h e nfin dxdot

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  5. Write the value of sin^(-1)(1/3)-cos^(-1)(-1/3) .

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  6. If 4\ sin^(-1)x+cos^(-1)x=pi , then what is the value of x ?

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  7. If x<0,\ y<0 such that x y=1 , then write the value of tan^(-1)x+ta...

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  8. What is the principal value of sin^(-1)(-(sqrt(3))/2)\ ?

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  9. Find the principal value of: sin^(-1)(-1/2)

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  10. Write the principal value of cos^(-1)(cos(2pi)/3)+sin^(-1)(s in(2pi)/3...

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  11. Write the value of tan(2tan^(-1)1/5) .

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  12. Write the principal value of tan^(-1)(1)+cos^(-1)(-1/2)

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  13. Write the value of tan^(-1)[2sin(2cos^(-1)(sqrt(3))/2)] .

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  14. Write the principal value of tan^(-1)sqrt((3))-cot^(-1)sqrt((-3)) .

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  15. Write the principal value of cos^(-1)[cos(680^0)]dot

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

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  17. The value of cos^(-1)(cos'(14pi)/(3)) is "…….."

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  18. Write the value of cos(sin^(-1)x+cos^(-1)x) , |x|lt=1 .

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  19. The value of tan((sin^(-1)x+cos^(-1)x)/(2)), when x = (sqrt(3))/(2), i...

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  20. The principal value of sin^(-1)[cos(sin^(-1)'1/2)] is pi/3.

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