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Question
Using the formula, tan 2A =`(2 tan A )/(1- tan^2 A)` find the value of tan 600, it being given that tan 300 = `1/sqrt(3)`.
Solution
A = 300
⇒ 2A = 2 × 300 = 600
By substituting the value of the given T-ratio, we get:
tan 2A = `(2 tan A )/(1- tan^2 A)`
`⇒ tan 60^0 = (2 tan 30^0)/(1- tan^2 30^0) = (2xx (1/sqrt(3)))/(1-(1/sqrt(3))^2 ` =` ((2/sqrt(3)))/(1-1/3) = ((2/sqrt(3)))/(2/3) = (2/sqrt(3))= 3/2 = sqrt(3) `
∴tan` 60^0 = sqrt(3)`.
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