Question

Решите тождество 2 sin^2 (45-2t) + sin 4t=1

Answer 1

$Formyla:; ; sin^2 alpha =frac{1-cos2 alpha }{2}; ; Rightarrow ; ; 2sin^2 alpha =1-cos2 alpha \\ alpha =45-2t; ; Rightarrow ; ; 2 alpha=90-4t\\cos2 alpha =cos(90-4t)=sin4t\\\2sin^2(45-2t)+sin4t=1-cos(90-4t)+sin4t=\\=1+sin4t-sin4t=1$