devarshi-dt-logo

Question:

Prove that tan(π/4 + x)tan(π/4 - x) = (1 + tan x)/(1 - tan x)²

Solution:

Use identity tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)
LHS = tan(π/4 + x)tan(π/4 - x) = (1 + tan x)/(1 - tan x) * (1 - tan x)/(1 + tan x)
LHS = (1 + tan x)/(1 - tan x)² = RHS
Hence proved