What is the value of cos θ · sec θ?
Answer and explanation
Correct answer: 1
The governing concept is the reciprocal relationship between cosine and secant. By definition, sec θ = 1/cos θ wherever cos θ is nonzero. Hence cos θ · sec θ = cos θ · (1/cos θ) = 1. Therefore option B is correct. This is a reciprocal cancellation, not a squaring operation. Option C would result from multiplying cos θ by itself, while option D would involve multiplying sec θ by itself. Option A is incorrect because a number and its reciprocal do not generally have product zero; their product is one. The usual domain condition is important: the expression is defined only when cos θ ≠ 0.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The governing concept is the reciprocal relationship between cosine and secant. By definition, sec θ = 1/cos θ wherever cos θ is nonzero. Hence cos θ · sec θ = cos θ · (1/cos θ) = 1. Therefore option B is correct. This is a reciprocal cancellation, not a squaring operation. Option C would result from multiplying cos θ by itself, while option D would involve multiplying sec θ by itself. Option A is incorrect because a number and its reciprocal do not generally have product zero; their product is one. The usual domain condition is important: the expression is defined only when cos θ ≠ 0.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
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