If sin A + sin^{2} A = 1 then what is the value of (1 – cos^{4} A)?

- 1
- sin
^{2}A - cos A
- cos
^{2}A

Option 4 : cos^{2} A

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sin A + sin^{2} A = 1

⇒ sin A = 1 – sin^{2} A

⇒ sin A = cos^{2} A

Squaring both sides, we get

⇒ sin^{2} A = cos^{4} A

⇒ 1 - cos^{2} A = cos^{4} A

⇒ cos^{2}A + cos^{4} A = 1

⇒ 1 – cos^{4} A = cos^{2} A

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