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.

the answer will be

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled