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Question
\[\frac{2 \tan 30° }{1 + \tan^2 30°}\] is equal to
Options
sin 60°
cos 60°
tan 60°
sin 30°
Solution
We have to find the value of the following expression
`(2 tan 3θ°)/(1+ tan^2 30°)`
`(2 tan 30°)/(1+tan ^2 30°)`
=`(2xx1/sqrt3)/(1+(1/sqrt3))`
= `(2/sqrt3)/(1+1/3)`
=`(2/sqrt3)/(4/3)`
Since tan 60°=`sqrt3/2` , since tan 30°= `1/sqrt3`
=`sqrt3/2`
= `sin 60°`
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