If sin A + sin2A = 1 then cos2A + cos4A = ?

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

If sin A + sin²A = 1 then cos²A + cos⁴A = ?

$\frac{1}{2}$

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Since, sin A + sin²A = 1 therefore, sin A = 1 - sin²A =cos²A

Hence, cos²A + cos⁴A = sin A + sin²A = 1