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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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