Answer:
Step-by-step explanation:
Let's break this down. The secant of a negative angle is the same as the secant of the positive angle. This is because secant is the inverse of cosine, and cosine is an even function. f(-x) = f(x) if the function is even, and f(-x) = -f(x) if the function is odd. Sine is odd and has symmetry about the origin; cosine is even and has y-axis symmetry.
Therefore, sec(-θ) = sec(θ) and we have then
sec(θ) - cos(θ). Since secant is the inverse of cosine, we can write:
[tex]\frac{1}{cos\theta}-cos\theta[/tex] and finding a common denominator:
[tex]\frac{1-cos^2\theta}{cos\theta}[/tex] and using a trig identity:
[tex]\frac{sin^2\theta}{cos\theta}[/tex] and simplify that down a bit by breaking it up:
[tex]\frac{sin\theta}{cos\theta}*sin\theta[/tex] finally boils down to
tanθ · sinθ, the last choice there.
