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L=sinα(cos²α+sin²α)=sinα*1=sinα
P=sin²α
L≠P
( może źle przepisałeś tożsamość )
b)tgα(sinα+cosα)²-2sin²α=tgα
L=tgα(sinα+cosα)²-2sin²α=tgα(sin²α+2sinαcosα+cos²α)-2sin²α=
=tgα(1+2sinαcosα)-2sin²α=tgα-tgα*2sinαcosα-2sin²α=
=tgα-(sinα/cosα)*2sinαcosα-2sin²α=tgα-2sin²α-2sin²α=tgα
P=tgα
L=P
voila!