Given that x is an obtuse angle and sin x =3/5, find, without the use of calculator, cos0.5x

please help me thanks. Also, i have something to clarify,in cases like this: solve for x between 0 to 180 deg

can i just cancel out cos x ? then i will have tan x =3/2 x=56.3

but since i cancel out the cos x so it is suppose to be zero so i just put cos x =0 and x=90

the zero part doesnt sound very logical to me.is it right to do that?