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Prove that tan(sin^-1 x) = (x/(sqrt 1-...

Prove that
`tan(sin^-1 x) = (x/(sqrt 1-x^2)), 1 x 1 < 1`

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. The value of the expressions (cos^(-1)x)^(2) is equal to sec^(2)x.

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  2. All trigonometric functions have inverse over their respective domains...

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  3. Prove that tan(sin^-1 x) = (x/(sqrt 1-x^2)), 1 x 1 < 1

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  4. True or False statements : cot(cos^-1 x) = x/(sqrt(1-x^2) for |x| le...

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  5. True or False statements : sin^-1 sqrtx + sec^-1 (1/sqrtx) = pi/2 fo...

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  6. The minimum value of n for which tan^(-1)""n/pi lt pi/4, n in N, is va...

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

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  8. The least numerical value, either positive or negative of angle theta ...

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  9. The graph of y = 6 is a line

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

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  11. The graph of inverse trigonometric function can be obtained from the g...

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  12. tan 1gttan^(-1) 1

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  13. Match the following

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  14. sin^-1 (sin y) = y if y lies in the interval

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  15. cos^-1 (sqrt3/2) is equal to

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  16. Domain of the function f (x) = sin^-1 x is equal to :

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  17. Domain of the function f (x) = tan^-1 x is equal to :

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  18. Which of the following is the principal value branch of cos^(-1)x ?

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  19. Which of the following is the principal value branch of cosec^(-1)x ?

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  20. sin (sin^-1 x + cos^-1 x) is equal to (-1 le x le 1)

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