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Demonstrati egalitatile: 1+sin[tex] \alpha [/tex]+cos[tex] \alpha [/tex]+tg[tex] \alpha [/tex]=(1+cos[tex] \alpha [/tex])(1+tg[tex] \alpha[/tex])

Răspuns :

[tex](1+cos\alpha)(1+tg\alpha)=1+tg\alpha+cos\alpha+cos\alpha\cdot tg\alpha=\\\\=1+tg\alpha+cos\alpha+cos\alpha\cdot\dfrac{sin\alpha}{cos\alpha}=1+sin\alpha+cos\alpha+tg\alpha.[/tex]

Green eyes.