Cos(3α)/sin(α) + sin(3α)/cos(α), если α=22°30'

Найти   cos(3α)/sin(α) + sin(3α)/cos(α) ,   если α=22°30'

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cos(3α)/sin(α) + sin(3α)/cos(α) =  

( cos(3α)*cos(α) sin(α) + sin(3α) *sin(α) )  / ( sin(α) *cos(α) )  =

cos(3α - α) / ( sin2(α) / 2 ) =2cos(2α) / sin2(α) =  2ctg2α   || α=22°30' || =

= 2ctg45°  = 2*1 = 2 .

сos(3α)/sin(α) + sin(3α)/cos(α)=2*(сos3α*cosα+sin3α*sinα)/sin2α=

2сos2α/sin2α=2*tg2α=2*tg45°=2