Oblicz 3sin2a - cos^2 3a / tg4a - 1/tg3a jesli a = 15 stopni a - alfa

[latex] alpha =15 stopni= frac{pi}{12} \ 2 alpha = frac{pi}{6} \ 3 alpha= frac{pi}{4} \ 4 alpha = frac{pi}{3} \ 3sin alpha - frac{cos^23 alpha }{tg4 alpha } - frac{1}{tg3 alpha }= 3sin frac{pi}{6} - frac{cos^2 frac{pi}{4} }{tg frac{ pi }{3} } - ctg frac{pi}{4}=\ =3* frac{1}{2} - frac{(frac{ sqrt{2} }{2})^2 }{sqrt{3}}-1= frac{3}{2} - frac{frac{1}{2} }{sqrt{3} }-1= frac{1}{2} -frac{sqrt{3}}{6}[/latex]

[latex]alpha = 15^o\\ 3sin2alpha - cfrac{cos^2 3alpha}{ an4alpha} - cfrac{1}{ an3alpha}=\\ = 3sin(2cdot15^o) - cfrac{cos^2 (3cdot15^o)}{ an(4cdot15^o)} - cfrac{1}{ an(3cdot15^o)}=\\ = 3sin30^o - cfrac{cos^2 45^o}{ an60^o} - cfrac{1}{ an45^o}=\\ = 3cdotfrac{1}{2} - cfrac{frac{1}{2}}{sqrt{3}} - cfrac{1}{1}= frac{3}{2}-frac{sqrt{3}}{6}-1=frac{1}{2}-frac{sqrt{3}}{6}=cfrac{3-sqrt{3}}{6}[/latex]