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Prove : 3sin^(-1)x=sin^(-1)(3x-4x^(3)...

Prove :
`3sin^(-1)x=sin^(-1)(3x-4x^(3))," "x in[-1/2,1/2]`

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The correct Answer is:
`therefore3thetain[-pi/2,pi/2]`
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KUMAR PRAKASHAN-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE - 2.2
  1. Prove : 3sin^(-1)x=sin^(-1)(3x-4x^(3))," "x in[-1/2,1/2]

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  2. Prove : 3cos^(-1)x=cos^(-1)(4x^(3)-3x),x in[1/2,1]

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

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  4. Prove : 2"tan"^(-1)1/2+"tan"^(-1)1/7="tan"^(-1)31/17

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  5. Write the following functions in the simplest form : tan^(-1)((sqrt(...

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  6. Write the following functions in the simplest form : tan^(-1)(1/(sqr...

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  7. Write the following functions in the simplest form : tan^(-1)(sqrt((...

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  8. Write the following functions in the simplest form : tan^(-1)((cosx-...

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  9. Write the following functions in the simplest form : "tan"^(-1)(x)/(...

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  10. Write the following functions in the simplest form : tan^(-1)((3a^(2...

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  11. Find the values of each of the following : tan^(-1)[2cos(2"sin"^(-1)...

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  12. Find the values of each of the following : cot[tan^(-1)a+cot^(-1)a]

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  13. Find the values of each of the following : "tan"1/2["sin"^(-1)(2x)/(...

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  14. If sin("sin"^(-1)1/5+cos^(-1)x)=1, then find the value of x.

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  15. If "tan"^(-1)(x-1)/(x-2)+"tan"^(-1)(x+1)/(x+2)=pi/4, then find the val...

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  16. Find the value of each of the expressions in sin^(-1)("sin"(2pi)/3)

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  17. Find the value of each of the expressions in tan^(-1)("tan"(3pi)/4)

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  18. Find the value of each of the expressions in tan("sin"^(-1)3/5+"cot"...

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  19. Select the proper option so that statement becomes true. cos^(-1)("c...

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  20. Select the proper option so that statement becomes true. sin(pi/3-si...

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