a) (1+cosα)(1-cosα)= sin²α
L=1²-cos²α=1-cos²α=sin²α+cos²α-cos²α=sin²α=P
b) ctg²α * (tg²α - sin²α)= sin²α
L=(cos²α/sin²α)*([sin²α/cos²α]-sin²α)=(cos²α/sin²α)*([sin²α(1-cos²α)]/cos²α)=(cos²α/sin²α)*(sin⁴α/cos²α)=sin⁴α/sin²α=sin²α=P
c)1+ctgα=(sinα+cosα):sinα
L=1+ctgα=1+cosα/sinα=sinα/sinα+cosα/sinα=(sinα+cosα)/sinα=P
d)1+tg²α=1/cos²α
L=1+tg²α=1+sin²α/cos²α=cos²α/cos²α+sin²α/cos²α=(sin²α+cos²α)/cos²α=1/cos²α=P