How do you simplify csc theta minus cot x theta times cos theta plus 1?

Answer 1

There can be no significant simplicfication if some of the angles are theta and others are x, so assume that all angles are x.

[csc(x) - cot(x)]*[cos(x) + 1]

=[1/sin(x) - cos(x)/sin(x)]*[cos(x) + 1]

=1/sin(x)*[1 - cos(x)]*[cos(x) + 1]

=1/sin(x)*[1 - cos2(x)]

=1/sin(x)*[sin2(x)]

= sin(x)