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

Prove the following:
`sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2))`

Answer

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Prove the following: sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2))

Prove that sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,(1)/(sqrt(2))lexle1 .

Knowledge Check

  • d/dx (sin^(-1) sqrt((1-x)/2)) =

    A
    `1/(sqrt(1-x^(2))`
    B
    `(-1)/(sqrt(1-x^(2))`
    C
    `1/(2 sqrt(1-x^(2))`
    D
    `(-1)/(2sqrt(1-x^(2))`

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    Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

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