Question

proof that sin60° =2tan30°/1+tan²30°

Answer 1

LHS = sin60° = sin2(30°)
we know,
sin2∅ = 2tan∅/(1 + tan²∅) use this
sin2(30°) = 2tan30°/(1 + tan²30°) = RHS

mehtod 2 :-
LHS = sin60° = √3/2
RHS = 2tan30°/(1 + tan²30°)
we know,
tan30° = 1/√3
= 2×1/√3/(1 + 1/3 )
= 2/√3/(4/3)
= 3×2/√3×4
=√3/2

hence,LHS = RHS