Hi,
there are some parenthesis that need to be changed and Sqrt is capitalised.
Solve[(1 - t)/(Sqrt[1 + t^2])*(Sqrt[2]) == 1/2, t]
gives
{{t -> 1/7 (8 - Sqrt[15])}}
or
{{t -> 0.589574}}
which is different from your solution.
In fact, your suggested solution does not appear to solve the equation:
In[90]:= (1 - t)/(Sqrt[1 + t^2])*(Sqrt[2]) == 1/2 /. t -> 2 - Sqrt[3]
Out[90]= False
In[93]:= (1 - t)/(Sqrt[1 + t^2])*(Sqrt[2]) == 1/2 /.
t -> 1/7 (8 - Sqrt[15]) // N
Out[93]= True
M.
