Answer:
[tex] \sqrt{6} [/tex]
Step-by-step explanation:
We want to evaluate:
[tex] \frac{ \tan(60 \degree) }{ \cos(45 \degree) } [/tex]
Recall from special angles that:
[tex] \tan(60 \degree) = \sqrt{3} [/tex]
[tex] \cos(45 \degree) = \frac{ \sqrt{2} }{2} [/tex]
We substitute these values into the given expression to get:
[tex] \frac{ \sqrt{3} }{ \frac{ \sqrt{2} }{2} } [/tex]
[tex] = \sqrt{3} \times \frac{2}{ \sqrt{2} } [/tex]
[tex] = 2 \sqrt{3} \times \frac{ \sqrt{2} }{2} [/tex]
[tex] = \sqrt{6} [/tex]
