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Question
If A = 30°, verify that `tan 2A = (2 tan A)/(1 - tan^2A)`.
Sum
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Solution
A = 300
⇒ 2A = 2 × 300 = 600
tan 2A = tan `60^0 = sqrt(3)`
`(2 tan A)/(1- tan^2 A) = (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))xx3/2 = sqrt(3)`
∴ tan 2A = `(2tanA)/(1-tan^2A)`
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Chapter 11: T-Ratios of Some Particular Angles - EXERCISE 11 [Page 572]
