simplify cos(θ) − sec(θ) /sin(θ)
Replace tan θ with sin θ/cos θ = sin²θ/cos θ + cos θ Now multiply the right-hand side by cos θ/cos θ to get the same denominator: = sin²θ/cos θ + cos²θ/cos θ = (sin²θ + cos²θ)/cos θ The numerator is equivalent to 1: = 1 / cos θ = sec θ
