we have that
tan (pi/2-x)=cot x
we know that
tan (pi/2-x)=[sin(pi/2-x)]/[cos(pi/2-x)]
[sin(pi/2-x)]=sin(pi/2)*cos x-cos(pi/2)*sin(x)
remember that
cos(pi/2)=0
sin(pi/2)=1
[sin(pi/2-x)]=cos x
and
[cos(pi/2-x)]=cos(pi/2)*cos(x)+sin(pi/2)*sin(x)
remember that
cos(pi/2)=0
sin(pi/2)=1
then
[cos(pi/2-x)]=sin(x)
substituting
tan (pi/2-x)=cosx/sinx
[cosx/sinx]=cot x
therefore
tan (pi/2-x)=cot x
the answer is
identity needs
tan x=(sin x/ cos x)
cos (A-B)=cos A*cos B+sin A*sin B
sin (A-B)=sin A*cos B-cos A*sin B
