1.Uprość wyrażenie : 3+(1 + tg(kwadrat)Aalfa) x cos (kwadrat) alfa.
2.Uzasadni nierówność: a) cos(kwadrat)alfa (tg(kwadrat)alfa+1)=1
b)(1+sin alfa) x (1/cos alfa- tg alfa)=cos alfa
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1. 3+(1+tg²α)*cos²α=3+cos²α+cos²α*tg²α=3+cos²α+sin²α/cos²α*cos²α=3+cos²α+sin²α=3 +1=4
2.
a) cos²α(tg²α+1)=1
L=cos²α(tg²α+1)=cos²α*tg²α+cos²α=cos²α*sin²α/cos²α +cos²α=sin²α+cos²α=1
P=1
L=P
b) (1+sinα)*(1/cosα-tgα)=cosα
L=(1+sinα)*(1/cosα-tgα)=(1+sinα)*(1/cosα-sinα/cosα)=(1+sinα)*(1-sinα)*1/cosα=(1-sin²α)*1/cosα=(sin²α+cos²α-sin²α)*1/cosα=cos²α*1/cosα=cosα
P=cosα
L=P