Simplify the expression using trigonometric identities: sec (–θ) – cos θ.

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:

and finding a common denominator:

and using a trig identity:

and simplify that down a bit by breaking it up:

finally boils down to

tanθ · sinθ, the last choice there.

a. is correct

the correct answer is x/3+10≥32

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