udowodnij tożsamości: a) (1÷sinα-1÷cosα)(tgα+ctgα)=(cosα-sinα)÷(sin²α×cos²α) L=(1÷sinα-1÷cosα)(sinα/cosα+cosα/sinα)= L=1÷sinα*sinα/cosα+ 1÷sinα*cosα/sinα- 1÷cosα* sinα/cosα-1÷cosα*cosα/sinα= 1/cosα+ cosα/sin²α- sinα/cos²α-1/sinα= [cosα*sin²α+cos³α-sin³α-cos²α*sinα]/(sin²α*cos²α)= [cosα*(1-cos²α)+cos³α-sin³α-(1-sin²α)*sinα]/(sin²α*cos²α)= [cosα-cos³α+cos³α-sin³α-sinα+sin³α]/(sin²α*cos²α)= [cosα-sinα]/(sin²α*cos²α)=P b) (cosα÷sinα)-(sinα÷cosα)=(ctgα-1)(tgα+1) P=(ctgα-1)(tgα+1)=ctgα*tgα+ctgα-tgα-1=1+ctgα-tgα-1=ctgα-tgα=P c) sin⁴α-cos⁴α=sin²α-cos²α L=sin⁴α-cos⁴α=(sin²α-cos²α)(sin²α+cos²α)=sin²α-cos²α=P d) (ctgα-tgα)÷(sinα+cosα)=1÷sinα-1÷cosα L=(ctgα-tgα)÷(sinα+cosα)=(cosα/sinα-sinα/cosα)÷(sinα+cosα)= [(cos²α-sin²α)/sinα*cosα]÷(sinα+cosα)= [(cosα-sinα)(cosα+sinα)/sinα*cosα]÷(sinα+cosα)= (cosα-sinα)(cosα+sinα)/sinα*cosα*(sinα+cosα)= (cosα-sinα)/sinα*cosα=cosα/sinα*cosα-sinα/sinα*cosα= 1/sinα-1/cosα=P
a) (1/sinα - 1/cosα)(tgα + ctgα) = (cosα - sinα)/(sin²α * cos²α) L = ((cosα - sinα)/cosα * sinα)(sinα/cosα + cosα/sinα) = ((cosα - sinα)/cosα * sinα)((sin²α + cos²α)/sinα * cosα) = (cosα - sinα)*(sin²α + cos²α)/cos²α * sin²α = (cosα - sinα)/cos²α * sin²α = P b) (cosα/sinα) - (sinα/cosα) = (ctgα - 1)(tgα + 1) P = (ctgα - 1)(tgα + 1) = ctgα * tgα - tgα + ctgα - 1 = ctgα * 1/ctgα - 1 - tgα + ctgα = 0 + (cosα/sinα) - (sinα/cosα) = (cosα/sinα) - (sinα/cosα) = L c) sin⁴α - cos⁴α = sin²α - cos²α L = sin⁴α - cos⁴α = (sin²α)² - (cos²α)² = (sin²α - cos²α)(sin²α + cos²α) = sin²α - cos²α = P d) (ctgα - tgα)/(sinα + cosα) = 1/sinα - 1/cosα L = ((cosα/sinα) - (sinα/cosα))/(sinα + cosα) = ((cos²α - sin²α)/sinα*cosα)/(sinα + cosα) = (cos²α - sin²α)/[sinα*cosα(sinα + cosα)] = (cosα - sinα)(sinα + cosα)/(sinα*cosα(sinα + cosα)) = (cosα - sinα)/sinα*cosα = 1/sinα - 1/cosα = P jak masz pytania to pisz na pw
udowodnij tożsamości a) 1+ctg a = sin a+ cos a /: sin a b) (1+ cos a)(1- cos a)=sin kwadrat a c) cos do potęgi4 a-sin do potęgi4 a = cos kwadrat a - sin kwadrat a...
Udowodnij poniższe tożsamości trygonometryczne: 1. (1 +sin α)/ cos α = cos α/(1 - sin α) 2. (1 +sinα) * (1/cos α - 1/ctgα) - cos α = 0 Z góry dzięki...
Udowodnij tożsamości trygonometryczne : a). (sin alfa + cos alfa)^2 + (sin alfa - cos alfa)^2 =2 b). tg alfa - ctg alfa = (tg alfa -1) (ctg alfa +1)...
