Question

FAST!! Evaluate tan60/cos45
√6
√3/2
√2/3
1√6

Answer 1

`√(6)`.

Explanation:

`(tan(60))/(cos(45))`

`= ((sin(60))/(cos(60)))/(cos(45))`

`= (sin(60))/(cos(60)*cos(45))`

`= ((√(3))/(2))/((1)/(2)*(√(2))/(2))`

`= ((√(3))/(2))/((√(2))/(4))`

`= (4√(3))/(2√(2))`

`= (2√(3))/(√(2))`

`= (2√(3)√(2))/(2)`

`=√(3)√(2)`

`=√(6)`.

Answer 2

`(\tan 60\degree)/(\cos45 \degree)= √(6)`

Explanation:

We want to evaluate

`(\tan 60\degree)/(\cos45 \degree)`

We use special angles or the unit circle to obtain;

`(\tan 60\degree)/(\cos45 \degree)=(√(3))/((√(2))/(2))`

This implies that;

`(\tan 60\degree)/(\cos45 \degree)=√(3)/ (√(2))/(2)`

`(\tan 60\degree)/(\cos45 \degree)=√(3)* √(2)`

`(\tan 60\degree)/(\cos45 \degree)= √(6)`