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For the principal value, evaluate tan...

For the principal value, evaluate `tan^(-1){2sin(4\ cos^(-1)(sqrt(3))/2)}`

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`tan^(-1){2sin(4\ cos^(-1)((sqrt(3))/2))}`
`tan^(-1){2sin((4 pi)/6)}`
`=tan^(-1)(2 sin(pi-pi/3))`
`=tan^(-1)(2 xx sqrt3/2)`
`=pi/3`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Find the principal value of each of the following: tan^(-1)(cos(pi/2...

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  2. For the principal value, evaluate tan^(-1)(-1)+cos^(-1)(-1/(sqrt(2)...

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  3. For the principal value, evaluate tan^(-1){2sin(4\ cos^(-1)(sqrt(3)...

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  4. Evaluate: tan^(-1)1+cos^(-1)(-1/2)+sin^(-1)(-1/2)

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  5. tan^(- 1)(-1/(sqrt(3)))+tan^(- 1)(-sqrt(3))+tan^(- 1)(sin(-pi/2))

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  6. Evaluate: tan^(-1)(tan((5pi)/6))+cos^(-1){cos(((13pi)/6))}

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  7. Find the principal value of sec^(-1)(2)

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

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  9. Find the set of values of sec^(-1)((sqrt(3))/2)

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  10. Find the principal values of sec^(-1)(2/(sqrt(3))) and sec^(-1)(-2)

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  11. Find the domain of sec^(-1)(2x+1) .

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  12. Find the principal values of each of the following: sec^(-1)(-sqrt(...

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  13. Find the principal values of each of the following: sec^(-1)(2sin((3...

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  14. For the principal value, evaluate tan^(-1)sqrt(3)-sec^(-1)(-2)

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  15. For the principal value, evaluate sin^(-1)(-(sqrt(3))/2)-2sec^(-1)(2...

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  16. Find the domain of sec^(-1)(3x-1) (ii) sec^(-1)x-tan^(-1)x

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  17. Find the domain of sec^(-1)(3x-1) (ii) sec^(-1)x-tan^(-1)x

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  18. Find the principal values of "c o s e c"^(-1)(2) and "c o s e c"^(-...

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  19. Find the set of values of "c o s e c"^(-1)(-1/2) .

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  20. For the principal values, evaluate the following: cot^(-1)(-1)+cos e ...

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