(1 - sinA)2 + (1 + sinA)2 + (1 - cosA)2 + (1 + cosA)2 எதற்குச் சமம்?

  1. √2
  2. 1/2
  3. 2
  4. 6

Answer (Detailed Solution Below)

Option 4 : 6
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Detailed Solution

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கொடுக்கப்பட்டவை,

(1 - sinA)2 + (1 + sinA)2 + (1 - cosA)2 + (1 + cosA)2

⇒ 1 + sin2A – 2 sinA + 1 + sin2A + 2 sinA + 1 + cos2A – 2 cosA + 1 + cos2A + 2 cosA (∵ (a ± b)2 = a2 ± 2ab + b2)

⇒ 1 + sin2A + 1 + sin2A + 1 + cos2A + 1 + cos2A

⇒ 4 + 2 (sin2A + cos2A)

⇒ 4 + 2 = 6 (∵ sin2A + cos2A = 1)

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