If α ∈ (π / 2, π) and sin α = 4 / 5, then the value of sin (α + π / 4) + cos (α + π) is?

If α ∈ (π / 2, π) and sin α = 4 / 5, then the value of sin (α + π / 4) + cos (α + π) is?


α ∈ (π / 2, π), and sin α = 4 / 5, then cos α = - 3 / 5
sin(α+π/4)+cos(α+π)
=sinαcos π/4+cosαsinπ/4-cosα
=4 / 5 * radical 2 / 2-3 / 5 * radical 2 / 2 - (- 3 / 5)
=Root 2 / 10 + 3 / 5



Find the value of sin [COS-1 4 / 5 - COS-1 (- 4 / 5)]
Need a process, thank you


The original formula = sin [cos-14 / 5 - (π - cos-14 / 5)]
=sin[2cos-1 4/5 -π]
=-sin[2cos-1 4/5]
=-2sin(cos-1 4/5)cos(cos-1 4/5)
=-2*3/5*4/5
=-24/25