Question

Cum calculez:
tg 75°-tg15°=?
imi explicati si mie va rog frumos?
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Answer 1

Răspuns:

Aplici formula tg(a+b)=(ta+tgb)/1-tga*tgb)

tg75=tg(30+45)=(tg30+tg45)/(1-tg30*tg45)=(√3/3+1)/(1-√3/3)=

[(√3+3)/3](3-√3)/3=(3+√3)/(3-√3)

tg15=tg(45-30)=(tg45-tg30)/(1+tg45*tg30)=

(1-√3/3)/(1+1*√3/3)=(3-√3)/(3+√3)

tg75-tg15=

(3+√3)/(3-√3)-(3-√3)/(3+√3)=

[(3+√3)²-(3-√3)²]/(3²-√3²)=

(9+6√3+3-9+6√3-3)/(9-3)=

6√3/6=√3

Explicație pas cu pas:

Answer 2

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