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Which of the following inverse trigonometric functions has the principal value range \(\left[0,\pi\right]\)?निम्नलिखित में से किस प्रतिलोम त्रिकोणमितीय फलन का प्रमुख मान-परास \,\(\left[0,\pi\right]\)\, है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\cos^{-1}x\)\(\cos^{-1}x\)
The principal value range of \(\cos^{-1}x\) is \([0,\pi]\), for \(-1\le x\le1\). In contrast, \(\sin^{-1}x\) has range \([-\pi/2,\pi/2]\). Exam tip: learn each inverse function’s domain together with its principal range.\(\cos^{-1}x\) का प्रमुख मान-परास \([0,\pi]\) होता है, जहाँ \(-1\le x\le1\)। इसके विपरीत \(\sin^{-1}x\) का परास \([-\pi/2,\pi/2]\) है। परीक्षा में प्रतिलोम फलनों के domain और principal range को साथ याद रखें।
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