Final answer:
The smallest value that sec²x can take is 1, which occurs when cos(x) is at its maximum value of 1.
Step-by-step explanation:
The question is asking for the smallest value that sec²x can take. The secant function, sec(x), is the reciprocal of the cosine function, cos(x). Therefore, sec²x is the square of the reciprocal of cos(x). Since the cosine function has values between -1 and 1 inclusive, the smallest value cos(x) can have is -1.
However, because we are taking the square of the secant function, we only consider the positive reciprocal. Hence, the smallest value sec(x) can take is the reciprocal of the largest value of cos(x), which is 1. Therefore, sec²x will also be 1 when cos(x) is 1. As such, the smallest value for sec²x is 1 which corresponds to option b).
The smallest value that sec²x takes is 1. This is because sec²x is the square of the secant function, and the secant function never goes below 1. The range of the secant function is (-∞, -1] ∪ [1, ∞), so the smallest possible value for sec²x is 1.
Therefore answer is d) There is no minimum value.