33) [tex] E=\frac{\sin{36}^\circ}{\sin{48}^\circ}+\frac{\cos{36^\circ}}{\cos{48^\circ}}=\frac{\sin36^\circ\cos48^\circ+\cos36^\circ\sin48^\circ}{\sin48^\circ\cos48^\circ}=\frac{\sin(36^\circ+48^\circ)}{\sin48^\circ\cos48^\circ}=\frac{\sin84^\circ}{\frac{1}{2}\sin(2\cdot48^\circ)}=2\frac{\sin(90^\circ-6^\circ)}{\sin(90^\circ+6^\circ)}=2\frac{\sin90^\circ\cos6^\circ-\cos90^\circ\sin6^\circ}{\sin90^\circ\cos6^\circ+\cos90^\circ\sin6^\circ}=2\frac{\cos6^\circ}{\cos6^\circ}=2 [/tex]
34) e doar o idee, nu duce la un rezultat frumos..
[tex] E=tg280^\circ tg170^\circ+\sin520^\circ\cos250^\circ-\sin110^\circ\cos20^\circ\\
tg280^\circ=tg(3\cdot90^\circ+10^\circ)=tg10$, pentru c\u a tangenta este periodic\u a de perioad\u a $T=k\pi, k\in\mathbb{Z}$, adic\u a $tg(k\pi+x)=tg x, \forall x [/tex]
[tex] tg170^\circ=tg(2\cdot90^\circ-10^\circ)=tg(-10^\circ)=-tg10^\circ\\
\cos520^\circ=\cos(2\cdot180^\circ+160^\circ)=\sin160^\circ=\sin(18^\circ-20^\circ)=-\sin20^\circ\\
\cos250=\cos(2\cdot180^\circ-110^\circ)=\cos110^\circ=\cos(90^\circ+20^\circ)=\cos90^\circ\cos20^\circ-\sin90^\circ\sin20^\circ=-\sin20^\circ\\
\sin110^\circ=\sin(90^\circ+20^\circ)=\sin90^\circ\cos20^\circ+\cos90^\circ\sin20^\circ=\cos20^\circ\\
E=-tg^210^\circ+\sin^220^\circ-\cos^220^\circ [/tex]
