Question

Evaluate:

`(5 tan 60^circ)/((sin^2 60^circ + cos^2 60^circ) tan 30^circ)`

Answer 1

Given: `(5 tan 60^circ)/((sin^2 60^circ + cos^2 60^circ) tan 30^circ)`

Step-wise calculation:

1. `sin 60^circ = sqrt(3)/2, cos 60^circ = 1/2`

So sin² 60° + cos² 60° = 1   ...(Pythagorean identity)

2. `tan 60^circ = sqrt(3)` and `tan 30^circ = 1/sqrt(3)`.

3. Substitute: `(5 xx sqrt(3))/(1 xx (1/sqrt(3)))` 

= `(5sqrt(3))/(1/sqrt(3))` 

= `5sqrt(3) xx sqrt(3)`

= 5 × 3

= 15