Question

证明这题左边等于右边，谢谢

Answer 1

证：
cos(45°-x)/[1+sin(2x)]
=sin[90°-(45°-x)]/(sin²x+cos²x+2sinxcosx)
=sin(x+45°)/(sinx+cosx)²
=sin(x+45°)/ {2[(√2/2)sinx+(√2/2)cosx]²}
=sin(x+45°)/{2(sinxcos45°+cosxsin45°)²}
=sin(x+45°)/[2sin(x+45°)²]
=1/[2sin(x+45°)]
=½csc(x+45°)

追问

第三个等于号那里就不明白了

追答

就是构造sin(x+45°)
sinx+cosx
=√2[(√2/2)sinx+(√2/2)cosx]
=√2(sinxcos45°+cosxsin45°)
=√2sin(x+45°) (和差角公式)
(sinx+cosx)²=[√2sin(x+45°)]²=2sin²(x+45°)
cos(45°-x)/[1+sin(2x)]
=sin(x+45°)/[2sin²(x+45°)]
=1/[2sin(x+45°)]
=½csc(x+45°)

Answer 2

骨灰盒把