Question

Sen(45°) - Sec(30°)= ?

Answer 1

$\mathrm{Expresar\:con\:seno,\:coseno}$

$\bold{=\sin \left(45^{\circ \:}\right)-\frac{1}{\cos \left(30^{\circ \:}\right)}}$

$\mathrm{Utilizar\:la\:siguiente\:identidad\:trivial}:\quad \sin \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}$

$\mathrm{Utilizar\:la\:siguiente\:identidad\:trivial}:\quad \cos \left(30^{\circ \:}\right)=\frac{\sqrt{3}}{2}$

$\bold{=\frac{\sqrt{2}}{2}-\frac{1}{\frac{\sqrt{3}}{2}}}$

$\mathrm{Simplificar}$

$\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\bold{=\frac{\sqrt{2}}{2}-\frac{2\sqrt{3}}{3}\begin{pmatrix}\mathrm{Decimal:}&-0.44759\dots \end{pmatrix}}}}}}}}$