Question
Download Solution PDF\({\sin ^{ - 1}}\left( {\sin \frac{{4\pi }}{5}} \right)\) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि \(x \in \left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]\) है, तो \({\sin ^{ - 1}}\ (sin x) = x\) है लेकिन यदि\(x{ \notin }\left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]\) है, तो प्रमुख शाखा के अंदर x का मान लाने के लिए\(\sin x = \sin \left( {\pi - x} \right)\) का प्रयोग कीजिए।
हल:
\({\sin ^{ - 1}}\left( {\sin \frac{{4\pi }}{5}} \right)\) but \(\frac{{4\pi }}{5}\notin{ }\left[ { - \frac{\pi }{2},\frac{\pi }{2}} \right]\)
इसलिए, संबंध का प्रयोग करने पर,
\(\sin \frac{{4\pi }}{5} = \sin \left( {\pi - \frac{{4\pi }}{5}} \right)\)
\(= \sin \left( {\frac{\pi }{5}} \right)\)
इसलिए,
\({\sin ^{ - 1}}\left( {\sin \frac{{4\pi }}{5}} \right) = {\sin ^{ - 1}}\left( {\sin \frac{\pi }{5}} \right)\)
\( = \frac{\pi }{5}\)
Last updated on May 30, 2025
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