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
