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Question
\[\frac{2 \tan 30°}{1 - \tan^2 30°}\] is equal to ______.
Options
cos 60°
sin 60°
tan 60°
sin 30°
Solution
\[\frac{2 \tan 30°}{1 - \tan^2 30°}\] is equal to tan 60°.
Explanation:
`(2 tan 30°)/(1-tan^2 30°)`
As, tan 30° = `1/sqrt3`
By substituting the value we get,
`= (2 xx 1/sqrt3)/(1-(1/sqrt3)^2)`
`= (2/sqrt3)/((3 - 1)/(3))`
`= 3/sqrt3`
`= (3sqrt3)/3`
`= sqrt3`
And, `sqrt3` = tan 60°.
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