Prove that

sin 2x(tan x + cot x) = 2


To Prove: sin 2x(tan x + cot x) = 2

Taking LHS,


sin 2x(tan x + cot x)


We know that,






We know that,


sin 2x = 2 sinx cosx



= 2(sin2x + cos2x)


= 2 × 1 [∵ cos2 θ + sin2 θ = 1]


= 2


= RHS


∴ LHS = RHS


Hence Proved


1