Question

Evaluate tan60degrees over cos45degrees

Answer 1

tan(60)/cos(45) = (sin(60)/cos(60))/cos(45)
= ((√3/2)/(1/2))/(√2/2) = (√3)/(√2/2) = (2√3)/(√2)
= ((2√3)(√2))/((√2)(√2)) = (2√6)/2 = √6

If any step doesn't makes sense, hmu!

Answer 2

`\sqrt6`

Explanation:

We are given that
`(tan60^(\circ))/(cos45^(\circ))`

We have to evaluate tan 60 degrees over cos 45 degrees

We know that
`tan 60=\sqrt3`

`cos45=(1)/(\sqrt2)`

Substitute the values then we get

`(tan60^(\circ))/(cos45^(\circ)) =(\sqrt3)/((1)/(\sqrt2))`

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

Suppose , we have

`(2)/((2)/(3))=(2* 3)/(2)=3`

Using this rule

`(tan60^(\circ))/(cos45^(\circ)) =\sqrt3* \sqrt2=\sqrt6`

`(tan60^(\circ))/(cos45^(\circ)) =\sqrt6`

Hence,
`(tan60^(\circ))/(cos45^(\circ)) =\sqrt6`