What is the general solution of cos100 x - sin100 x = 1?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. nπ 
  2. (2n + 1)π 
  3. 2nπ
  4. (2n + 1)π / 2

Answer (Detailed Solution Below)

Option 1 : nπ 
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Detailed Solution

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Explanation:

cos100x – sin100x = 1 is only possible when cos2 x = 1 or sin2 x = 0

because cos2 x ∈ [0, 1]

⇒ cos100x ∈  [0, 1]

Also  sin2∈ [0, 1] 

⇒  sin100∈ [0, 1] 

⇒ Cos2x = 1

⇒ x = nπ ± 0°

x = nπ 

∴ The correct answer is option 1.

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