Question

33 si 34 va rog urgent!:))

Answer 1

33) $E=\frac{\sin{36}^\circ}{\sin{48}^\circ}+\frac{\cos{36^\circ}}{\cos{48^\circ}}=\frac{\sin36^\circ\cos48^\circ+\cos36^\circ\sin48^\circ}{\sin48^\circ\cos48^\circ}=\frac{\sin(36^\circ+48^\circ)}{\sin48^\circ\cos48^\circ}=\frac{\sin84^\circ}{\frac{1}{2}\sin(2\cdot48^\circ)}=2\frac{\sin(90^\circ-6^\circ)}{\sin(90^\circ+6^\circ)}=2\frac{\sin90^\circ\cos6^\circ-\cos90^\circ\sin6^\circ}{\sin90^\circ\cos6^\circ+\cos90^\circ\sin6^\circ}=2\frac{\cos6^\circ}{\cos6^\circ}=2$

34) e doar o idee, nu duce la un rezultat frumos..

$E=tg280^\circ tg170^\circ+\sin520^\circ\cos250^\circ-\sin110^\circ\cos20^\circ\\ tg280^\circ=tg(3\cdot90^\circ+10^\circ)=tg10 , pentru c\u a tangenta este periodic\u a de perioad\u a T=k\pi, k\in\mathbb{Z} , adic\u a tg(k\pi+x)=tg x, \forall x$

$tg170^\circ=tg(2\cdot90^\circ-10^\circ)=tg(-10^\circ)=-tg10^\circ\\ \cos520^\circ=\cos(2\cdot180^\circ+160^\circ)=\sin160^\circ=\sin(18^\circ-20^\circ)=-\sin20^\circ\\ \cos250=\cos(2\cdot180^\circ-110^\circ)=\cos110^\circ=\cos(90^\circ+20^\circ)=\cos90^\circ\cos20^\circ-\sin90^\circ\sin20^\circ=-\sin20^\circ\\ \sin110^\circ=\sin(90^\circ+20^\circ)=\sin90^\circ\cos20^\circ+\cos90^\circ\sin20^\circ=\cos20^\circ\\ E=-tg^210^\circ+\sin^220^\circ-\cos^220^\circ$