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Daca tg x = 1/3, calculati : 2sinx + 3cosx totul supra cos^3x - sin^3x. (^3 = la puterea a 3-a).


Multumesc.


Răspuns :

Tgx=1/3 deci sinx/cosx =1/3 deci sinx=1p iar cosx=3p
Atunci calculul tau devine R= (2*1p+3*3p)/(27*p^3-1*p^3)=10p/26p^3=5/13p^2
Cum sin^2+cos^2=1 rezulta ca p^2+9p^2=1
10p^2=1 deci p^2=1/10
Revenind la expresia noastra R=(5/13)*10=50/13