Question

calcular : E=tg30°sec60°-sen37°cos30°/(sen45°)

Answer 1

Calcular : E=tg30°sec60°-sen37°cos30°/(sen45°)

Hola!!

Pasamos a las funciones trigonométricas conocidas, es decir, a seno y a coseno, entonces

$E= tg\ 30\º* sec\ 60\º-sen\ 30\º*cos\ 30\º/(sen\ 45\º)\\\\E=\frac{sen\ 30\º}{cos\ 30\º}*\frac{1}{cos\ 60\º}-sen\ 30\º*cos\ 30\º/(sen\ 45\º)\\\\\\E= \dfrac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}*\dfrac{1}{\frac{1}{2}}-\frac{1}{2}*\frac{\sqrt{3} }{2}:\frac{\sqrt{2}}{2}\\\\\\E= \dfrac{1}{\frac{\sqrt{3}}{2}}-\frac{\sqrt{3} }{4}:\frac{\sqrt{2}}{2}\\\\\\E= \dfrac{2}{\sqrt{3}}-\frac{\sqrt{3} }{2\sqrt{2}}\\\\\\E= \dfrac{2*2\sqrt{2}-\sqrt{3}*\sqrt{3}}{\sqrt{3}*2\sqrt{2}}$

$E= \dfrac{4\sqrt{2}-\sqrt{3}^2}{2\sqrt{6}}\\\\\\E= \dfrac{4\sqrt{2}-3}{2\sqrt{6}}\\\\\\E= \dfrac{4\sqrt{2}-3}{2\sqrt{6}}*\dfrac{\sqrt{6}}{\sqrt{6}}\\\\\\E= \dfrac{4\sqrt{2}*\sqrt{6}-3*\sqrt{6}}{2\sqrt{6}^2}\\\\\\E= \dfrac{4\sqrt{12}-3\sqrt{6}}{2*6}\\\\\\E= \dfrac{4*2\sqrt{3}-3\sqrt{6}}{12}\\\\\\E=\dfrac{8}{12}\sqrt{3}-\dfrac{3}{12}\sqrt{6}\to\boxed{E=\frac{2}{3}\sqrt{3}-\frac{1}{4}\sqrt{6}}$

Espero que te sirva, salu2!!!!