Question:
The value of \(\cos(\sec^{-1}x+\text{cosec}^{-1}x)\), \(|x|\ge 1\) is
The value of \(\cos(\sec^{-1}x+\text{cosec}^{-1}x)\), \(|x|\ge 1\) is
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sec⁻¹x + cosec⁻¹x is always π/2 for |x| ≥ 1.
Updated On: Sep 23, 2026
- 1
- 0
- -1
- \(\dfrac{1}{2}\)
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The Correct Option is B
Solution and Explanation
Step 1: Key identity:
For every \(x\) with \(|x|\ge 1\), \(\sec^{-1}x+\text{cosec}^{-1}x=\dfrac{\pi}{2}\) (standard complementary inverse-trig identity).
Step 2: Substituting:
So \(\cos(\sec^{-1}x+\text{cosec}^{-1}x)=\cos\dfrac{\pi}{2}\).
Final Answer:
\(\cos\dfrac{\pi}{2}=0\).\[ \boxed{0} \]
For every \(x\) with \(|x|\ge 1\), \(\sec^{-1}x+\text{cosec}^{-1}x=\dfrac{\pi}{2}\) (standard complementary inverse-trig identity).
Step 2: Substituting:
So \(\cos(\sec^{-1}x+\text{cosec}^{-1}x)=\cos\dfrac{\pi}{2}\).
Final Answer:
\(\cos\dfrac{\pi}{2}=0\).\[ \boxed{0} \]
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