For 0° ≤ θ < 90°, the maximum value of 1/secθ is
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We are tasked with finding the maximum value of 1/secθ for 0° ≤ θ < 90°.
Step 1: Recall the definition of secant
The secant function is defined as:
secθ = 1/cosθ.
Thus, the reciprocal of secant is:
1/secθ = cosθ.
Step 2: Analyze the behavior of cosθ in the given range
For 0° ≤ θ < 90°:
– The cosine function decreases from cos 0° = 1 to cos 90° = 0 (but does not actually reach 0 since θ < 90°).
– Therefore, the maximum value of cosθ occurs at θ = 0°.
At θ = 0°:
cos 0° = 1.
Step 3: Conclusion
The maximum value of 1/secθ is equal to the maximum value of cosθ, which is 1.
The correct answer is:
a) 1
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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