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The value of tan((sin^(-1)x+cos^(-1)x)/(...

The value of `tan((sin^(-1)x+cos^(-1)x)/(2))`, when `x = (sqrt(3))/(2)`, is `"……."`.

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Verified by Experts

The correct Answer is:
`1`
`tan((sin^(-1)x+cos^(-1)x)/(2)) = tan'((pi//2)/(2)) , [:' sin^(-1)x + cos^(-1) x = pi/2]`
` = tan ' pi/4 = 1`
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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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