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Show that sin^(-1)(2xsqrt(1-x^2))=2sin^(...

Show that `sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x`

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Given,
`sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x`
Let `x=cosy`
`(2xsqrt(1-x^2))=2xsqrt(1-cos^2y)`
`=sin2y`
thus,
`sin^(-1)(2xsqrt(1-x^2))`
...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Write the value of tan^(-1)a/b-tan^(-1)((a-b)/(a+b))

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  2. Write the value of cos^(-1)(cos(5pi)/4) .

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  3. Show that sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x

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

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  5. If tan^(-1)(sqrt(3))+cot^(-1)x=pi/2 , find xdot

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  6. If sin^(-1)(1/3)+cos^(-1)x=pi/2,t h e nfin dxdot

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  7. Write the value of sin^(-1)(1/3)-cos^(-1)(-1/3) .

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  8. If 4\ sin^(-1)x+cos^(-1)x=pi , then what is the value of x ?

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  9. If x<0,\ y<0 such that x y=1 , then write the value of tan^(-1)x+ta...

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  10. What is the principal value of sin^(-1)(-(sqrt(3))/2)\ ?

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  11. Find the principal value of: sin^(-1)(-1/2)

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  12. Write the principal value of cos^(-1)(cos(2pi)/3)+sin^(-1)(s in(2pi)/3...

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  13. Write the value of tan(2tan^(-1)1/5) .

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  14. Write the principal value of tan^(-1)(1)+cos^(-1)(-1/2)

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  15. Write the value of tan^(-1)[2sin(2cos^(-1)(sqrt(3))/2)] .

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  16. Write the principal value of tan^(-1)sqrt((3))-cot^(-1)sqrt((-3)) .

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  17. Write the principal value of cos^(-1)[cos(680^0)]dot

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

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

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  20. Write the value of cos(sin^(-1)x+cos^(-1)x) , |x|lt=1 .

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