Write the expression in terms of sine and cosine, and then multiply so that no quotients appear in the final expression and all functions are of theta only.

Question

1-tan(- theta)/ tan(- theta)

Answer 1

(1 - tan(-θ)) / tan(-θ)

Since tanθ is an odd function, tan(-θ) = -tanθ

So, we have (1 + tanθ) / (-tanθ) = [(1 + sinθ / cosθ] / [-sinθ / cosθ]

= [ (cosθ + sinθ) / cosθ ] / [-sinθ / cosθ ]

= (cosθ + sinθ) / (-sinθ) = -cosθ / sinθ - sinθ / sinθ = -cotθ - 1

Answer 2

As written the answer is 0.