cos100 x - sin100 x = 1 का सामान्य हल क्या है?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. (2n + 1)π
  2. 2nπ
  3. (2n + 1)π / 2

Answer (Detailed Solution Below)

Option 1 : nπ
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NDA 01/2025: English Subject Test
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व्याख्या:

cos100x - sin100x = 1 तभी संभव है जब cos2 x = 1 या sin2 x = 0 हो। 

क्योंकि cos2 x ∈ [0, 1]

⇒ cos100x ∈ [0, 1]

इसके अलावा sin2 x ∈ [0, 1]

⇒ sin100x ∈ [0, 1]

⇒ Cos2x = 1

⇒ x = nπ ± 0°

x = nπ

∴ सही उत्तर विकल्प 1 है।

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