Step-by-step explanation:
We know that tan=sin/cos, so tan(x+π/2)=
[tex]\frac{sin(x+pi/2)}{cos(x+pi/2)}[/tex]
Then, we know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v),
so our equation is then
[tex]\frac{sin(x)cos(\pi/2)+cos(x)sin(\pi/2)}{cos(x+\pi/2)} = \frac{cos(x)}{cos(x+\pi/2) }[/tex]
Then, cos(u+v)=cos(u)cos(v)-sin(u)sin(v), so our expression is then
[tex]\frac{cos(x)}{cos(x)cos(\pi/2)-sin(x)sin(\pi/2)} = \frac{cos(x)}{-sin(x)} = -cot(x)[/tex]
