Question

Prove that: 2tan3001+tan300=2cos300-sin600

Answer 1

Step-by-step explanation:

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