If tan + sin = m and tan - sin = n , Show that (m^2 – n^2 )^2 = 16 mn .
(m²-n²)²
=>{(tanA + sinA)² - (tan A - sinA)²}²
=> {4tanAsinA}²
=>16tan²A sin²A
RHS:16(tanA+sinA)(tanA-sinA)
=>16 ( tan²A - sin²A)
=>16 (sin²A/cos²A - sin²A)
=>16 { (sin²A - sin²Acos²A)/cos²A}
=>16 sin²A(1 - cos²A)/cos²A
=>16 sin²Asin²A / cos²A
=>16tan²Asin²A
LHS=RHS