Question

How do you simplify `(cosx-sin(pi/2-x)sinx)/(cosx-cos(pi-x)tanx)`?

Answer 1

Simplify trig expression

Explanation:

Property of complementary arcs -->
`sin (pi/2 - x) = cos x`
Property of supplementary arcs -->
`cos (pi - x) = - cos x`
`tan x = sin x/(cos x)`
The expression becomes:
`E = (cos x - cos x.sin x)/(cos x + sin x) =`
`= (cos x(1 - sin x))/(cos x + sin x)`