Question

If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2A)`.

Answer 1

A = 30⁰ 
⇒ 2A = 2 × 30⁰  = 60⁰ 

sin 2A = sin `60^0 = sqrt(3)/2`

`(2 tan A)/(1+tan^2A)= (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)))/(4/3)=(2/sqrt(3)) xx 3/4=sqrt(3)/2`

∴ sin 2A = `(2 tan A)/(1+tan^2 A)`