1. sin α = √(1-(cosα)^2)= √(1-16/25)= √(9/25)=3/5
tg α = sin α/cos α=3/5*(-5/4)=-3/4
cos 2α = (cos α)^2 - (sin α)^2 = 16/25 - 9/25 = 7/25
2. cos 135 = -cos 45 = -√2/2
sin (8π/3) = 2*sin (4π/3)*cos(4π/3) = 2*sin 240*cos 240 = 2*sin 60*cos 60 = 2* √3/2*1/2 = √3/2
tg (7π/3) = tg 240 = tg 60 = √3
(cos π/8)^2 - (sin π/8)^2 = cos (2* π/8) = cos ( π/4) = cos 45 = √2/2
3. 1) = sin α*cos β - sin β*cos α + sin β*cos α = sin α*cos β
2) = (cos (π-α) + cos (π/2-α))* (cos (π-α) - cos (π/2-α)) = (-cos α + sin α)*(-cos α - sin α) = (cos α - sin α)*(cos α + sin α) = (cos α)^2 - (sin α)^2 = cos 2α
3) = sin α*sin β + cos α*cos β - sin α*sin β = cos α*cos β = cos (α-β)