cos²α+sin²α=1 tgα*ctgα=1 sinα/cosα=tgα cosα/sinα=ctgα 1. (cos α/sinα + tgα) × sin²α = tgα L=(cos α/sinα + tgα) × sin²α=(cos α/sin α+ sin α/cos α)× sin²α= ((cos²α+sin²α)/(sinα*cosα))*sin²α= (1*sin²α)/(sinα*cosα)= sinα/cosα=tgα=P 2. ((1+(cosα/sinα)²)/1+tg²α ) × tg²α = 1 L=((1+(cosα/sinα)²)/1+tg²α ) × tg²α= =((1+ctg²α)/(1+tg²α))*tg²α= =(tg²α+ctg²α*tg²α)/((1+tg²α)= =(tg²α+1)/(1+tg²α)=1=P
1. (cos α/sinα + tgα) × sin²α = tgα Korzystam ze wzorów: cosα/sinα=ctgα sinα/cosα=tgα tgα*ctgα=1 cos²α+sin²α=1 ( jedynka trygonometryczna L=(cos α/sinα + tgα)*sin²α L =(cos α/sin α+ sin α/cos α)* sin²α wspólny mianownik to : sinα*cosα L =[(cos²α+sin²α):(sinα*cosα)]*sin²α L = (1*sin²α) :(sinα*cosα) redukuje się sinα w liczniku i mianowniku L =sinα:cosα L =tgα P =tgα L = P jest to tożsamość 2. ((1+(cosα/sinα)²)/(1+tg²α ) × tg²α = 1 L=[(1+(cosα/sinα)²]:(1+tg²α ) × tg²α L =[(1+ctg²α): (1+tg²α)]*tg²α L = tg²α(1+ctg²α) : (1+tg²α) L =(tg²α + tg²α*ctg²α) : (1+tg²α) L =(tg²α + 1) : (1 + tg²α) L =(tg²α + 1) : (tg²α +1 ) L = 1 P = 1 L = P jest to tożsamość
