Question

Sin (180+x)cos (90+x)tan (270-x)cot (360-x)÷sin (360-x)cos(360+x)cosec (-x)sin (270+x)=1

Answer 1

sin(180+x)=-sinx
cos(90+x)=-sinx
tan(270-x)=cotx
cot(360-x)=-cotx
sin(360-x)=-sinx
cos(360+x)=cosx
cosec(-x)=-cosecx
sin(270+x)=-cosx

therefore,

sin(180+x)cos(90+x)tan(270-x)cot(360-x)÷sin(360-x)cos(360+x)cosec(-x)sin(270+x)

=(-sinx)(-sinx)(cotx)(-cotx)÷(-sinx)(cosx)(-cosecx)(-cosx)

=(-sin x)(-sinx)(cosx/sinx)(-cosx/sinx)÷(-sinx)(cosx)(-1/sinx)(-cosx)

=1