Вычислите √2sinπ/4+√2cosπ/4=???

Question

Вычислите √2sinπ/4+√2cosπ/4=???

Answer 1

√2sinπ/4+√2cosπ/4=2(√2/2sinπ/4+√2/2cosπ/4);
√2/2=cosπ/4;√2/2=sinπ/4;⇒
2(cosπ/4·sinπ/4+sinπ/4·cosπ/4)=2·sin(π/4+π/4)=2·sinπ/2=2·1=2;