sec2 A + (cosec2 A - 1) - (1 + tan2 A) - cot2 A = ______.

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  1. sec2 A
  2. 0
  3. cot2 A
  4. 1

Answer (Detailed Solution Below)

Option 2 : 0
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दिया गया है:

sec2 A + (cosec2 A - 1) - (1 + tan2 A) - cot2 A = __

प्रयुक्त अवधारणा:

पाइथागोरस त्रिकोणमितीय सर्वसमिकाएँ:

cosec2 θ - 1 = cot2 θ

1 + tan2 θ = sec2 θ

गणना:

⇒ sec2 A + (cosec2 A - 1) - (1 + tan2 A) - cot2 A

त्रिकोणमितीय सर्वसमिकाओं के अनुसार मान रखने पर,

⇒ sec2 A + cot2 A - sec2 A - cot2 A = 0

इसलिए, sec2 A + cot2 A - sec2 A - cot2 A का आवश्यक मान 0 है।

अतः सही उत्तर विकल्प (2) है।

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