Question

oblicz:

(tg 135 +tg 150)* (tg45 + tg30)

wynik 2/3

Answer 1

Korzystam ze wzorów redukcyjnych dla α∈(0, 90°)

(tg135°+tg150°)*(tg45°+tg30°)=

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tg135°=tg(180°-45°)=-tg45°

tg150°=tg(180°-150°)=-tg30°

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=(-tg45°-tg30°)(tg45°+tg30°)=

=-(tg45°+tg30°)(tg45°+tg30°)=

=-(tg45°+tg30°)²=

=-(1+√3/3)²=

=-[(1+√3)/3]²=

=-[(1+2√3+3)/9]=

=-[(4+2√3)/9]

Answer 2

(-1+ (-pierw3/3)) * (1+ pier3/3)

-1 -pierw3/3 - pierw3/3= -1 + 3/3 (czyli 1)= -1 + 1 = 0