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Question
`(2 tan 30°)/(1+tan^2 30°)` = ______.
Options
sin 60°
cos 60°
tan 60°
sin 30°
Solution
`(2 tan 30°)/(1+tan^2 30°)` = sin 60°.
Explanation:
`(2 tan 30°)/(1+tan^2 30°)`
= `(2(1/sqrt3))/(1+(1/sqrt3)^2)`
= `(2/sqrt3)/(1+1/3)`
= `(2/sqrt3)/(4/3)`
= `6/(4sqrt3)`
= `sqrt3/2`
Out of the given alternatives, only sin 60° = `sqrt3/2`
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