Question

If A = 30⁰ , verify that:

(iii) tan 2A = `(2tanA)/(1-tan^2A)`

Answer 1

A = 30⁰ 
⇒ 2A = 2 × 30⁰  = 60⁰ 

(iii) 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)`