Pre-Calc help ???

Question

need to verify this equation: sec(theta)-1/1-cos(theta) = sec(theta)

Answer 1

To simplify notation, instead of theta I'll use t. We know sec(t) = 1/cos(t). Multiplying the numerator and the denominator by cos(t), it follows that

(sec(t)-1)/(1-cos(t)) = (1 - cos(t))/(cos(t) - cos(t)^2) =(1 - cos(t))/(cos(t)(1 - cos(t))) = 1/cos(t) = sec(t), as desired.