If a = 30°, Verify that Sin 2a = (2 Tan A)/(1 + Tan^2 A)

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

Sum

LHS = sin 2A
Putting A = 30° in LHS and RHS., we get
LHS = sin 2 x 30° = sin 60° = `sqrt3/2`

RHS = `(2 xx tan 30°)/(1 + tan^2 30°) = (2 xx 1/sqrt3)/( 1 + (1/sqrt3)^2)`

= `(2/sqrt3)/(1 + 1/3). (2/sqrt3)/(4/3)`

= `(2 xx 3)/(sqrt3 xx 4) = sqrt3/4`
Hence,
LHS = RHS
Hence proved.

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