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show that tan(1/2 sin-1 3/4) = 4-root7/3

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take sin-1 3/4 = a;

then LHS = tan (a/2);

RHS = (4 - root 7 )/3;

divide nu and dr by 4

which gives ( 1- root7/4 ) / (3/4)

sin a = 3/4; so root7/4 = cos a;

RHS = (1-cos a)/ sin a;

= 2 (sin a/2) ^2 / 2sin(a/2)cos(a/2);

= tan (a/2) = LHS

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