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Prove the following : sin^(-1)(2xsqrt(...

Prove the following :
`sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,x in[-1/sqrt2,1/sqrt2]`

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KUMAR PRAKASHAN-INVERSE TRIGONOMETRIC FUNCTIONS-PRACTICE WORK
  1. Find the values of the followings : sin^(-1)(1/sqrt2)-3"sin"^(-1)sqr...

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  2. Find the values of the followings : tan^(-1)(1)+cos^(-1)(-1/sqrt2)

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  3. Prove the following : sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,x in[-1/s...

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  4. Prove the following : "tan"^(-1)2/11+"tan"^(-1)7/24="tan"^(-1)1/2

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  5. Prove the following : "tan"^(-1)1/4+"tan"^(-1)2/9="tan"^(-1)1/2

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  6. Write the following functions in the simplest from : tan^(-1)((cosx)...

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  7. Write the following functions in the simplest from : sin^(-1)(2xsqrt...

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  8. Write the following functions in the simplest from : sin^(-1)(x^(2)s...

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  9. Write the following functions in the simplest from : cot^(-1)(sqrt(1...

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  10. Write the following functions in the simplest from : cot^(-1)(1/sqrt...

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  11. Find the values of each of the following : sin(2"cos"^(-1)4/5)

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  12. Find the values of each of the following : tan^(2)(1/2"cos"^(-1)3/4)

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  13. Find the values of each of the following : sin(pi/2-"cos"^(-1)3/7)+c...

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  14. Find the values of each of the following : tan^(-1)2x+tan^(-1)(1/(x+...

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  15. Find the values of each of the following : sin(cos^(-1)sqrt3x+cos^(-...

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  16. Find the values of each of the following : tan[sin^(-1)(3/5)+cos^(-1...

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  17. Find the value of sin^(-1)("cos"pi/8).

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  18. Find the value of tan^(-1)("tan"(5pi)/4).

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  19. Find the value of sin(2"tan"^(-1)4/3).

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  20. Find the value of sin[tan^(-1)("tan"(7pi)/6)]+cos[cos^(-1)("cos"(7pi...

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