Simplify the Expression

Question

Simplify the expression fully:

-sin(t)/tan(t) - tan(t)/sin(t) = _____

Answer 1

-sint/tant - tant/sint

=-sint/(sint/cost) - (sint/cost)/sint

=-sint(cost/sint) - 1/cost

= -cost -sect

Answer 2

Tan = sin/cos, so replace tan in both terms with that and you get

Sin/(sin/cos) - (sin/cos)/sin

Flip and multiply both terms to get sin/1 * cos/sin - sin/cos*1/sin

In both terms, the sin on top cancels with the sin on the bottom so you get cos - 1/cos. You can simplify this to cos(t)-sec(t)

Answer 3

Conver tan t to sin t / cos t, reduce and subtract