Wzory pomocnicze: tgx=sinx/cosx ctgx=cosx/sinx sin²x+cos²x=1 a) cosx+tgx/sinx*cosx=1/sinx + 1/cos²x [cosx+(sinx/cosx)]/sinx*cosx=1/sinx + 1/cos²x [(cos²x+sinx)/cosx]/(sinx*cosx)=1/sinx + 1/cos²x (cos²x+sinx)/sinx*cos²x=1/sinx + 1/cos²x [cos²x/sinx*cos²x]+[sinx/sinx*cos²x]=1/sinx + 1/cos²x 1/sinx + 1/cos²x=1/sinx + 1/cos²x L=P b) sinα/(1+cosα) + (1+cosα)/sinα = 2/sinα [sin²α+(1+cosα)²]/[sinα*(1+cosα)] = 2/sinα [sin²α+1+2cosα+cos²α]/sinα*(1+cosα) = 2/sinα [sin²α+cos²α+1+2cosα]/sinα*(1+cosα) = 2/sinα [1+1+2cosα]/sinα*(1+cosα) = 2/sinα [2+2cosα]/sinα*(1+cosα) = 2/sinα 2(1+cosα) /sinα*(1+cosα) = 2/sinα 2/sinα= 2/sinα L=P c) sinα-sin³α/cosα-cos³α=ctgα sinα(1-sin²α)/[cosα(1-cos²α)]=ctgα [sinα*cos²α]/[cosα*sin²α]=ctgα [cos²α/cosα]*[sinα/sin²α]=ctgα cosα*1/sinα=ctgα cosα/sinα=ctgα ctgα=ctgα L=P d) cos²α=1+cos²α/2 /*2 2cos²α=1+cos²α cos²α=1 L≠P
a)cosx+tgx/sinx*cosx=1/sinx + 1/cos²x [cosx+(sinx/cosx)]/sinx*cosx=1/sinx + 1/cos²x [(cos²x+sinx)/cosx]/(sinx*cosx)=1/sinx + 1/cos²x (cos²x+sinx)/sinx*cos²x=1/sinx + 1/cos²x [cos²x/sinx*cos²x]+[sinx/sinx*cos²x]=1/sinx + 1/cos²x 1/sinx + 1/cos²x=1/sinx + 1/cos²x L=P b)sinα/(1+cosα) + (1+cosα)/sinα = 2/sinα [sin²α+(1+cosα)²]/[sinα*(1+cosα)] = 2/sinα [sin²α+1+2cosα+cos²α]/sinα*(1+cosα) = 2/sinα [sin²α+cos²α+1+2cosα]/sinα*(1+cosα) = 2/sinα [1+1+2cosα]/sinα*(1+cosα) = 2/sinα [2+2cosα]/sinα*(1+cosα) = 2/sinα 2(1+cosα) /sinα*(1+cosα) = 2/sinα 2/sinα= 2/sinα L=P c)sinα-sin³α/cosα-cos³α=ctgα sinα(1-sin²α)/[cosα(1-cos²α)]=ctgα [sinα*cos²α]/[cosα*sin²α]=ctgα [cos²α/cosα]*[sinα/sin²α]=ctgα cosα*1/sinα=ctgα cosα/sinα=ctgα ctgα=ctgα L=P d)cos²α=1+cos²α/2 /*2 2cos²α=1+cos²α cos²α=1 L≠P
hmmmm... bardzo trudne zadanie
