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Question
If θ = 30° verify that `sin 2theta = (2 tan theta)/(1 + tan^2 theta)`
Solution
Given θ = 30° ....(1)
To veriy
`sin 2theta = (2 tan theta)/(1 + tan^2 theta)` ....(2)
`sin 2 theta = sin 2 xx 30`
= sin 60
`= sqrt3/2`
Now consider right hand side
`(2 tan theta)/(1 + tan^2 theta) = (2 tan 30)/(1 + tan^2 30)`
`= (2 xx 1/sqrt3)/(1 + (1/sqrt3)^2)`
`= sqrt3/2`
Hence it is verified that,
`sin 2theta = (2 tan theta)/(1 + tan^2 theta)`
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