P + Q = π/4 হলে (1 + tanP)(1 + tanQ) = ?

ব্যাখ্যা

P + Q = π/4 ∴ Q = π/4 − P ∴ (1 + tanP){1 + tan(π/4 − P)} = (1 + tanP){1 + (tan(π/4) − tanP)/(1 + tan(π/4) tanP)} = (1 + tanP)·(1 + tanP + 1 − tanP)/(1 + tanP) = 1 + 1 = 2