Comprehension

निम्न दो (02) प्रश्नों के लिए निम्नलिखित पर विचार कीजिए :
माना कि   है। 

y किसके बराबर है?

This question was previously asked in
NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. sin-1x
  2. sin-1
  3. 3sin-1x
  4. 3sin-1

Answer (Detailed Solution Below)

Option 4 : 3sin-1
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Detailed Solution

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गणना:

दिया गया है,

फलन है, और हमें इसे सरल करना है।

हम देखते हैं कि हम व्यंजक को इस प्रकार गुणनखंडित कर सकते हैं:

इस प्रकार, फलन बन जाता है:

यह देखते हुए कि यह प्रतिलोम त्रिकोणमितीय फलनों के लिए एक ज्ञात सर्वसमिका के अनुरूप है:

इस प्रकार, हम व्यंजक को सरल कर सकते हैं:

इसलिए, सही उत्तर विकल्प 4 है।

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