Question

关于三角函数

关于三角函数化简

Answer 1

这样

Answer 2

cos40°/(cos25°√1-sin40°)
=cos40°/[cos25°√(cos20°-sin20°)^2]
=cos40°/[cos25°(cos20°-sin20°)]
=(cos20°-sin20°)(cos20°+sin20°)/[cos25°(cos20°-sin20°)]
=(cos20°+sin20°)/cos25°
=√2 (cos20°sin45+sin20°cos45)/cos25°
=√2sin65°/cos25°
=√2

Answer 3

cos40°/[cos25°√(1-sin40°)]

=cos40°/[cos25°√(1-cos50°)]
=cos40°/[cos25°√(2sin²25°)]
=cos40°/(√2sin25°cos25°)
=√2cos40°/(2sin25°cos25°)
=√2cos40°/sin50°
=√2cos40°/cos40°
=√2