Mathematics: Evaluate tan60degrees over cos45degrees

Evaluate tan60degrees over cos45degrees

luap6897

15.03.2022

$\sqrt6$

Step-by-step explanation:

We are given that $\frac{tan60^{\circ}}{cos45^{\circ}}$

We have to evaluate tan 60 degrees over cos 45 degrees

We know that $tan 60=\sqrt3$

$cos45=\frac{1}{\sqrt2}$

Substitute the values then we get

$\frac{tan60^{\circ}}{cos45^{\circ}} =\frac{\sqrt3}{\frac{1}{\sqrt2}}$

When a denominator in fraction then the number in the denominator of denominator fraction will convert into multiply

Suppose , we have

$\frac{2}{\frac{2}{3}}=\frac{2\times 3}{2}=3$

Using this rule

$\frac{tan60^{\circ}}{cos45^{\circ}} =\sqrt3\times \sqrt2=\sqrt6$

$\frac{tan60^{\circ}}{cos45^{\circ}} =\sqrt6$

Hence, $\frac{tan60^{\circ}}{cos45^{\circ}} =\sqrt6$

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