Answer:
[tex]\sqrt6[/tex]
Step-by-step explanation:
We are given that [tex]\frac{tan60^{\circ}}{cos45^{\circ}}[/tex]
We have to evaluate tan 60 degrees over cos 45 degrees
We know that [tex]tan 60=\sqrt3[/tex]
[tex]cos45=\frac{1}{\sqrt2}[/tex]
Substitute the values then we get
[tex]\frac{tan60^{\circ}}{cos45^{\circ}} =\frac{\sqrt3}{\frac{1}{\sqrt2}}[/tex]
When a denominator in fraction then the number in the denominator of denominator fraction will convert into multiply
Suppose , we have
[tex]\frac{2}{\frac{2}{3}}=\frac{2\times 3}{2}=3[/tex]
Using this rule
[tex]\frac{tan60^{\circ}}{cos45^{\circ}} =\sqrt3\times \sqrt2=\sqrt6[/tex]
[tex]\frac{tan60^{\circ}}{cos45^{\circ}} =\sqrt6[/tex]
Hence, [tex]\frac{tan60^{\circ}}{cos45^{\circ}} =\sqrt6[/tex]
