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Mathematics

If cos A + cos2 A = 1, then sin2 A + sin4 A is :

  1. 1

  2. 2

  3. 3

  4. 4

Trigonometric Identities

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Answer

cos A + cos2 A = 1

⇒ 1 - cos2 A = cos A

⇒ sin2 A = cos A

Given,

⇒ sin2 A + sin4 A

⇒ sin2 A + (sin2 A)2

⇒ sin2 A + cos2 A [∵ sin2 A = cos A]

⇒ 1.

Hence, option 1 is the correct option.

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