Question

Simplify the following, tan -x cos -x

Answer 1

Tan(A)=sin(A) / cos(A)
so
tan(A)*cos(A)=sin(A)/cos(A)*cos(A)
=sin(A)  [ by cancelling cos(A) ]

substitute -x for A, then
tan(-x)cos(-x) = sin(-x)  
[ provided cos(-x) does not equal zero, i.e. x does not equal (k+1/2)pi where k is an integer ]