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# Q.solve the following:Sin-1 + cos -1√1-4x2 = ∏/3(square root is on whole 1-4x2)

jitender lakhanpal
62 Points
9 years ago

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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