化简下列式子 cos(pai/4+a)+sin(pai/4+a)哥哥姐姐的详解
网友回答
cos(pai/4+a)+sin(pai/4+a)
=cos(π/4+a)+sin(π/4+a)
= cosπ/4•cos a -sinπ/4•sin a+ sinπ/4•cos a+cosπ/4•sin a
=√2/2•cos a -√2/2•sin a+ √2/2•cos a+√2/2•sin a
=√2/2•cos a + √2/2•cos a
=2*√2/2 cos a
=√2 cos a
提示：用和差化积公式化简,π/4=45°,cos45= sin45=√2/2