若α∈(π/2,π),且sinα=4/5,则sin(α+π/4)-√2/2cosα=

问题描述:

若α∈(π/2,π),且sinα=4/5,则sin(α+π/4)-√2/2cosα=

若α∈(π/2,π),且sinα=4/5,则cosα=-35
sin(α+π/4) - √2/2cosα=
=sinαcosπ/4+cosαsinπ/4- √2/2 cosα
=4/5*√2/2+(-3/5)*√2/2-√2/2*(-3/5)
=√2/2*(4/5)
=2√2/5

α∈(π/2,π)且sinα=4/5
所以cosα=-3/5
sin(α+π/4)-√2/2cosα
=sinαcosπ/4+cosαsinπ/4-√2/2cosα
=√2/2sinα+√2/2cosα-√2/2cosα
=√2/2sinα
=√2/2 ×4/5
=2√2/5