Question

Punctul c de la E3
VA ROG MULTTT​❤️❤️

Answer 1

Explicație pas cu pas:

sin 390° = sin (360°+30°) = sin 30°

cos 390° = cos (360°+30°) = cos 30°

tg 405° = tg (360°+45°) = tg 45°

...

$E = \dfrac{\sin \ 390^{0} + \cos \ 390^{0} + tg \ 405^{0}}{\sin \ 405^{0} + \cos \ 405^{0} + tg \ 390^{0}} =$

$= \dfrac{\sin \ 30^{0} + \cos \ 30^{0} + tg \ 45^{0}}{\sin \ 45^{0} + \cos \ 45^{0} + tg \ 30^{0}}$

$= \dfrac{\dfrac{1}{2} + \dfrac{ \sqrt{3} }{2} + 1}{\dfrac{ \sqrt{2} }{2} + \dfrac{ \sqrt{2} }{2} + \dfrac{ \sqrt{3} }{3}} = \dfrac{\dfrac{3 + \sqrt{3} }{2}}{\dfrac{3 \sqrt{2} + \sqrt{3} }{3}}$

$= \dfrac{3(3 + \sqrt{3})}{2(3 \sqrt{2} + \sqrt{3})} = \dfrac{3(3 + \sqrt{3})(3 \sqrt{2} - \sqrt{3})}{2(3 \sqrt{2} + \sqrt{3})(3 \sqrt{2} - \sqrt{3})}$

$= \dfrac{3(9 \sqrt{2} - 3 \sqrt{3} + 3 \sqrt{6} - 3)}{2(18 - 3)}$

$= \dfrac{3(3 \sqrt{2} - \sqrt{3} + \sqrt{6} - 1)}{10}$