(cosx⼀2)⼀根号(1+sinx)+(sinx⼀2)⼀根号(1-sinx) x∈(3π⼀3,2π)

2025-02-24 00:10:50
推荐回答(2个)
回答1:

x∈(3π/2,2π)

x/2∈(3π/4,π)
(cosx/2)/根号(1+sinx)+(sinx/2)/根号(1-sinx)

=[(cosx/2)√(1-sinx)+(sinx/2)√(1+sinx)]/√[(1-sinx)(1+sinx)]
=[cosx/2*|sinx/2-cosx/2|+sinx/2*|sinx/2+cosx/2|]/|cosx|
=[cosx/2*(sinx/2-cosx/2)-sinx/2*(sinx/2+cosx/2)]/(cosx)
=[-cos²x/2-sin²x/2]/cosx
=-1/cosx

回答2:

x的范围?