If sinA + sin2A = 1 then what is the value of cos2A + cos4A?

If sinA + sin²A = 1 then what is the value of cos²A + cos⁴A?

Given,

sinA + sin²A = 1

⇒ sinA = 1 – sin²A = cos²A      ----(1)    (? sin²θ + cos²θ = 1)

Squaring on both sides

sin²A = cos⁴A      ----(2)

Substitute (1) and (2) in the given expression.

cos²A + cos⁴A = sinA + sin²A = 1

∴ cos²A + cos⁴A = 1

Given,

sinA + sin²A = 1

⇒ sinA = 1 – sin²A = cos²A      ----(1)    (? sin²θ + cos²θ = 1)

Squaring on both sides

sin²A = cos⁴A      ----(2)

Substitute (1) and (2) in the given expression.

cos²A + cos⁴A = sinA + sin²A = 1

∴ cos²A + cos⁴A = 1

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