化简:cosα+sinα+a²sin(α+π/4)

问题描述:

化简:cosα+sinα+a²sin(α+π/4)

cosα+sinα+a²sin(α+π/4)
=cosα+sinα+a²(sinαcosαπ/4 +cosαsinπ/4)
=cosα+sinα+a²(sinα√2/2 +cosα√2/2)
=cosα+sinα+√2/2 a²(cosα+sinα)
=cosα+sinα(1+√2/2 a²)