Final answer:
Options b) csc(0°) and c) sec(90°) are undefined because both involve division by zero, which is not possible. Option a) sec(45°) is defined. Therefore, 'None of the above' is not the correct answer.
Step-by-step explanation:
The question asks us to identify which of the given options are undefined. We need to determine the values of sec(45°), csc(0°), and sec(90°) to ascertain which of them, if any, is undefined.
For option a), sec(45°) is defined as the reciprocal of cos(45°). Since cos(45°) is √2/2, its reciprocal sec(45°) will be 2/√2, which simplifies to √2. Therefore, sec(45°) is defined.
For option b), csc(0°) is the reciprocal of sin(0°), which is 0. Since you cannot divide by zero, csc(0°) is undefined.
For option c), sec(90°) is the reciprocal of cos(90°), which is 0. Similarly to b), since the division by zero is not possible, sec(90°) is also undefined.
Therefore, the correct answers are b) csc(0°) and c) sec(90°), as both are undefined. Option d) 'None of the above' is incorrect because two of the provided options are indeed undefined