QUESTION $4$

Using the substitution $t=tan(\frac{x}{2})$ with ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2dx}{cosx-sinx-1}=2ln|\frac{1}{t-1}|+C2ln|\frac{t^2-1}{t}|+C2ln|\frac{t+1}{t}|+C\frac{2(t^2-1)}{t}+C\frac{2}{t-1}+C-,$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2dx}{cosx-sinx-1}=$

$A.2ln|\frac{1}{t-1}|+C$

$B.2ln|\frac{t^2-1}{t}|+C$

$C.2ln|\frac{t+1}{t}|+C$

$D.\frac{2(t^2-1)}{t}+C$

$E.\frac{2}{t-1}+C$