1) cos(α+β) +2sinα*sinβ α - β = π .
а) cos(α+β) +2sinα*sinβ =cosα*cosβ -sinα*sinβ +2sinα*sinβ =
cosα*cosβ + sinα*sinβ =cos(α -β) =cosπ = -1.
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б) sin²α +(sin(π -α)*cos(π/2 -α))/(tq(π+α)*ctq(3π/2-α) ; α≠πn/2 ;n∈ Z.
sin²α +(sinα*sinα)/(tq*tqα) =sin²α +(sinα/cosα)² =sin²α +cos²α =1.
2)
sin2004°*cos1974° -sin1974°*cos2004° =sin(2004° -1974°) =sin30° =1/2.
3)
sinα =0,8 ; π/2 <α <π.<br>а) cosα = - √(1 - sin²α) = - √(1-0,8²) = - √(1-0,64) = - √0,36 = -0,6.
б) sin2α =2sinα*cosα =2*0,8*(-0,6) = - 0,96.
в) cos2α =cos²α - sin²α = 1- 2sin²α = 1 -2*(0,8)² =1 -2*0,64 = 1 -1,28 = - 0,28 .