Question

(sin2@+3cos2@)^2 + (cos2@-3sin2@)^2
помогите пожалуйста...​

Answer 1

$(Sin2\alpha+3Cos2\alpha)^{2} +(Cos2\alpha-3Sin2\alpha )^{2}=\\\\=Sin^{2}2\alpha+6Sin2\alpha Cos2\alpha +9Cos^{2}2\alpha+Cos^{2}2\alpha -6Sin2\alpha Cos2\alpha+9Sin^{2}2\alpha=\\\\=\underbrace{(Sin^{2}2\alpha+Cos^{2}2\alpha)}_{1}+9\underbrace{(Sin^{2}2\alpha+Cos^{2}2\alpha)}_{1}=1+9\cdot1=\boxed{10}$