Question

Evaluate:

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

Answer 1

Given:

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

`tan 60^@ = sqrt3, "so" tan^2 60^@ = (sqrt3)^2 = 3`.

`sin 60^@ = (sqrt3)/2, "so" sin^2 60^@ = ((sqrt3)/(2))^2 = 3/4`.

`cos 30^@ = (sqrt3)/(2), "so" cos^2 30^@ = ((sqrt3)/(2))^2 = 3/4`.

`sin^2 60^@ + cos^2 30^@ = 3/4 + 3/4 = 6/4 = 3/2`

`3/(3/2)`

 = `3 xx 2/3`

= 2