Q.solve the following:

Sin^-1 + cos ^-1√1-4x² = ∏/3

(square root is on whole 1-4x²)

Dear SHOBHIT,

AS WE KNOW

  COS^-1 X =SIN^{- 1  √}  1-X²

SO WE CAN WRITE  COS^-1√ 1-4X²  =SIN^-1( 2X)

                                                  =SIN^-1-( 2X)

WE GET SIN^-1( 2X)+SIN^-1( X)=    ∏/3----EQUATION 1  AND      SIN^-1( 2X)-SIN^-1( X)=    ∏/3   ----EQUATION 2

SOLVING EQUATION 1 

SIN^-1( 2X) = ∏/3- SIN^-1( X)

2X = SIN∏/3 COS(SIN^-1( X) ) - COS ∏/3 SIN(SIN^-1( X))

2X = √3/2  ^√  1-X² -(1/2)X

FROM THE ABOVE EQUTION WE GET X = -1/2

AND SIMILARLY WE GET OTHER VALUES BY SOLVING THE EQUTION 2 

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