Question

Simplify cos(θ) − sec(θ) / sin(θ)

Answer 1

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