If cos A + cos²A =1, then find the value of sin²A +sin⁴A
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It is given that cos A + cos² A = 1
=> cos A = 1 - cos² A
=> cos A = sin² A ••••••••••• (i)
Now, sin² A + sin⁴ A = sin² A + (sin² A)²
=> sin² A + cos² A = 1. [from (i)]
Therefore, the required answer is 1.
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