Verified answer

(cos(θ) -1) / sin(θ)

= - (1 - cos(θ)) / sin(θ)

= - 2 sin²(θ/2) / (2 sin(θ/2) cos(θ/2))

= - sin(θ/2) / cos(θ/2)

= - tan(θ/2).

(cos θ -1)/(sin θ)

= ±(cosθ - 1)/√(1-cos²θ)

= ±(1-cosθ)/√(1-cos²θ)

= ±(1-cosθ)/√[(1-cosθ)(1+cosθ)]

= ±√[(1-cosθ)/(1+cosθ)]

(Choose negative value for θ in quadrant 1 and 2, negative value for θ in quadrant 3 and 4)

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i've got not got a theta sign, so I used x particularly... (tanx)/(cosx-secx) make each thing in terms of sinx and cosx put in ideal places (sinx cosx)/[cosx(cosx-a million)] boost the backside (sinx cosx)/(cosx^2 - cosx) get rid of a cosx from each term (sinx)/(cosx-a million)