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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
[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