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The domain of trigonometric functions ...

The domain of trigonometric functions can be restricted to any one of their branch (not necessary principal value) in order to obtain their inverse function s.

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We know that, the domain of trigonometri functions are restricted in their domain to obtain their inverse functions.
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Read the following text and answer the following questions on the basis of the same : The value of an inverse trigonometric functions which lies in the range of Principal branch is called the principal value of that inverse trigonometric functions. Principal value of tan^(-1)(-1/sqrt3)

Properties of inverse trigonometric function part -2

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The graph of inverse trigonometric function can be obtained from the graph of their corresponding function by interchanging X and Y-axes.

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NCERT EXEMPLAR-INVERSE TRIGONOMETRIC FUNCTIONS-Inverse Trigonometric Functions
  1. The number of real solutions of the equation sqrt(1+cos2x) = sqrt(2)...

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  2. If cos^(-1)x gt sin^(-1) x, then

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  3. The principal value of cos^(-1)(-1/2) is

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

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  5. If cos(tan^(-1)x+cot^(-1)sqrt(3))=0 , find the value of xdot

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  6. The set of values of sec^(-1)(1/2) is "……….."

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  7. The principal value of tan^(-1)sqrt(3) is "……."

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

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  9. The value of cos(sin^(-1)x + cos^(-1)x), where |x| le 1, is

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

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  11. If y = 2tan^(-1)x+sin^(-1)((2x)/(1+x^(2))), then "………"lt y lt "………".

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  12. The result tan^(-1)x-tan^(-1)y = tan^(-1)((x-y)/(1+xy)) is true whe...

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  13. The value of cot^(-1)(-x) x in R in terms of cot^(-1)x is "…….."

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  14. All trigonometric functions have inverse over their respective domai...

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  15. The value of the expression (cos^(-1)x)^(2) is equal to sec^(2)x.

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  16. The domain of trigonometric functions can be restricted to any one o...

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  17. The least numerical value, either positive or negative of angle thet...

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  18. The graph of inverse trigonometric function can be obtained from th...

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  19. The minimum value of n for which tan^(-1)'n/pi gt (pi)/(4), n in N, i...

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

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