Question

√8.Csc45º + 10.Cos37º

Answer 1

$Expresar\:con\:seno,\:coseno:\csc \left(45^{\circ \:}\right)=\frac{1}{\sin \left(45^{\circ \:}\right)}$

$\bold{ =\sqrt{8\cdot \frac{1}{\sin \left(45^{\circ \:}\right)}+10\cos \left(37^{\circ \:}\right)}}$

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

$\bold{=\sqrt{\frac{8+10\cdot \frac{\sqrt{2}}{2}\cos \left(37^{\circ \:}\right)}{\frac{\sqrt{2}}{2}}}}$

$SIMPLIFICAR$

$\boxed{\bold{ =\sqrt{\sqrt{2}\left(8+5\sqrt{2}\cos \left(37^{\circ \:}\right)\right)}}}$