Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
Grade 12
Question:
<p>If \(\sin^{-1}a + \sin^{-1}b + \sin^{-1}c = \pi\), then the value of \(a\sqrt{1-a^2} + b\sqrt{1-b^2} + c\sqrt{1-c^2}\) will be</p>
<p>(a) \(2abc\)</p>
<p>(b) \(abc\)</p>
<p>(c) \(\frac{1}{2}abc\)</p>
<p>(d) \(\frac{1}{3}abc\)</p>
Step-by-Step Solution
Key Concept: Analyze the constraint that sum of inverse sines equals π and use trigonometric identities
<p>Given $\sin^{-1}a + \sin^{-1}b + \sin^{-1}c = \pi$, this implies specific relationships between the values using inverse sine properties.</p>
Correct Answer: A