Trigonometry & Inverse Trigonometry
Value of expressions
Grade 11
Question:
<p><strong>Question 586.</strong> The value of '<em>m</em>' is equal to:</p>
<p>(a) \(\dfrac{\pi^2}{3}\)</p>
<p>(b) \(\dfrac{\pi^2}{4}\)</p>
<p>(c) \(\dfrac{\pi^2}{6}\)</p>
<p>(d) \(\dfrac{\pi^2}{12}\)</p>
Step-by-Step Solution
Key Concept: Recognize that inverse trigonometric functions have restricted ranges, and use the relationship between sin⁻¹(x) and cos⁻¹(x): sin⁻¹(x) + cos⁻¹(x) = π/2 for x ∈ [-1,1].
<p><strong>Step 1:</strong> Identify the standard relationship for inverse trigonometric functions. For x ∈ [-1, 1], we have: sin⁻¹(x) + cos⁻¹(x) = π/2</p><p><strong>Step 2:</strong> Similarly, tan⁻¹(x) + cot⁻¹(x) = π/2 for all real x, and sec⁻¹(x) + cosec⁻¹(x) = π/2 for |x| ≥ 1</p><p><strong>Step 3:</strong> Apply the appropriate complementary relationship based on the given expression in the question to find the value of 'm'.</p><p><strong>Step 4:</strong> Verify that the result satisfies the range constraints of the inverse trigonometric function involved.</p><p>∴ Answer: C</p>
Correct Answer: C