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

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

Hola!

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

<img src="https://tex.z-dn.net/?f=E%3D%20tg%5C%2030%5C%C2%BA%2A%20sec%5C%2060%5C%C2%BA-sen%5C%2030%5C%C2%BA%2Acos%5C%2030%5C%C2%BA%2F%28sen%5C%2045%5C%C2%BA%29%5C%5C%5C%5CE%3D%5Cfrac%7Bsen%5C%2030%5C%C2%BA%7D%7Bcos%5C%2030%5C%C2%BA%7D%2A%5Cfrac%7B1%7D%7Bcos%5C%2060%5C%C2%BA%7D-sen%5C%2030%5C%C2%BA%2Acos%5C%2030%5C%C2%BA%2F%28sen%5C%2045%5C%C2%BA%29%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D%2A%5Cdfrac%7B1%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D-%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%7D%3A%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%7D-%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B4%7D%3A%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D-%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B2%5Csqrt%7B2%7D%7D%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B2%2A2%5Csqrt%7B2%7D-%5Csqrt%7B3%7D%2A%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B3%7D%2A2%5Csqrt%7B2%7D%7D" /><img src="https://tex.z-dn.net/?f=E%3D%20%5Cdfrac%7B4%5Csqrt%7B2%7D-%5Csqrt%7B3%7D%5E2%7D%7B2%5Csqrt%7B6%7D%7D%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B4%5Csqrt%7B2%7D-3%7D%7B2%5Csqrt%7B6%7D%7D%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B4%5Csqrt%7B2%7D-3%7D%7B2%5Csqrt%7B6%7D%7D%2A%5Cdfrac%7B%5Csqrt%7B6%7D%7D%7B%5Csqrt%7B6%7D%7D%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B4%5Csqrt%7B2%7D%2A%5Csqrt%7B6%7D-3%2A%5Csqrt%7B6%7D%7D%7B2%5Csqrt%7B6%7D%5E2%7D%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B4%5Csqrt%7B12%7D-3%5Csqrt%7B6%7D%7D%7B2%2A6%7D%5C%5C%5C%5C%5C%5CE%3D%20%5Cdfrac%7B4%2A2%5Csqrt%7B3%7D-3%5Csqrt%7B6%7D%7D%7B12%7D%5C%5C%5C%5C%5C%5CE%3D%5Cdfrac%7B8%7D%7B12%7D%5Csqrt%7B3%7D-%5Cdfrac%7B3%7D%7B12%7D%5Csqrt%7B6%7D%5Cto%5Cboxed%7BE%3D%5Cfrac%7B2%7D%7B3%7D%5Csqrt%7B3%7D-%5Cfrac%7B1%7D%7B4%7D%5Csqrt%7B6%7D%7D" />

Espero que te sirva, salu2!