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Question
`(2 tan 30°)/(1-tan^2 30°)` = ______.
Options
cos 60°
sin 60°
tan 60°
sin 30°
Solution
`(2 tan 30°)/(1-tan^2 30°)` = tan 60°
Explanation:
`(2 tan 30°)/(1-tan^2 30°)`
= `(2(1/sqrt3))/(1-(1/sqrt3)^2)`
= `(2/sqrt3)/(1-1/3)`
= `(2/sqrt3)/(2/3)`
= `sqrt3`
Out of the given alternatives, only tan 60° = `sqrt3`
Hence, tan 60° is correct.
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