Which of the following is not defined?

To determine which of the given trigonometric expressions is not defined, we analyze each option based on the definitions and properties of trigonometric functions.

Step 1: Analyze each option

a) cos 0°
The cosine function is defined for all real numbers. The value of cos 0° is:
cos 0° = 1.
Thus, cos 0° is defined.

b) tan 45°
The tangent function is defined as tan θ = sin θ / cos θ. For θ = 45°:
tan 45° = sin 45° / cos 45° = (1/√2) / (1/√2) = 1.
Thus, tan 45° is defined.

c) sec 90°
The secant function is defined as sec θ = 1 / cos θ. For θ = 90°:
cos 90° = 0.
Since division by zero is undefined, sec 90° = 1 / cos 90° = 1 / 0 is not defined.
Thus, sec 90° is not defined.

d) sin 90°
The sine function is defined for all real numbers. The value of sin 90° is:
sin 90° = 1.
Thus, sin 90° is defined.

Step 2: Final Answer
The expression that is not defined is:
c) sec 90°.
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.

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https://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/