[tex]Expresar\:con\:seno,\:coseno:\csc \left(45^{\circ \:}\right)=\frac{1}{\sin \left(45^{\circ \:}\right)}[/tex]
[tex]\bold{ =\sqrt{8\cdot \frac{1}{\sin \left(45^{\circ \:}\right)}+10\cos \left(37^{\circ \:}\right)}}[/tex]
[tex]\mathrm{Utilizar\:la\:siguiente\:identidad\:trivial}:\quad \sin \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}[/tex]
[tex]\bold{=\sqrt{\frac{8+10\cdot \frac{\sqrt{2}}{2}\cos \left(37^{\circ \:}\right)}{\frac{\sqrt{2}}{2}}}}[/tex]
[tex]SIMPLIFICAR[/tex]
[tex]\boxed{\bold{ =\sqrt{\sqrt{2}\left(8+5\sqrt{2}\cos \left(37^{\circ \:}\right)\right)}}}[/tex]
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[tex]Expresar\:con\:seno,\:coseno:\csc \left(45^{\circ \:}\right)=\frac{1}{\sin \left(45^{\circ \:}\right)}[/tex]
[tex]\bold{ =\sqrt{8\cdot \frac{1}{\sin \left(45^{\circ \:}\right)}+10\cos \left(37^{\circ \:}\right)}}[/tex]
[tex]\mathrm{Utilizar\:la\:siguiente\:identidad\:trivial}:\quad \sin \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}[/tex]
[tex]\bold{=\sqrt{\frac{8+10\cdot \frac{\sqrt{2}}{2}\cos \left(37^{\circ \:}\right)}{\frac{\sqrt{2}}{2}}}}[/tex]
[tex]SIMPLIFICAR[/tex]
[tex]\boxed{\bold{ =\sqrt{\sqrt{2}\left(8+5\sqrt{2}\cos \left(37^{\circ \:}\right)\right)}}}[/tex]