What is the simplified for of the expression cos theta / csc theta - sin theta?

How do you show your work on this?

1 answer

since cscθ = 1/sinθ,

cosθ/cscθ - sinθ
= cosθ sinθ - sinθ
= sinθ(cosθ-1)

or maybe you meant
cosθ/(cscθ-sinθ)
= cosθ/(1/sinθ - sinθ)
= cosθ sinθ / (1 - sin^2θ)
= cosθ sinθ / cos^2θ
= sinθ/cosθ
= tanθ

parentheses can make a difference!