Question

How can I set each side equal to each other?

Answer 1

RTP: [a tan(u) + b]² + [b tan(u) - a]² = (a² + b²) sec²(u)

Proving LHS = RHS:

LHS = [a tan(u) + b]² + [b tan(u) - a]²

= a² tan²(u) + 2ab tan(u) + b² + b² tan²(u) - 2ab tan(u) + a²
= (a² + b²) tan²(u) + (a² + b²)
= (a² + b²)[tan²(u) + 1]
= (a² + b²) sec²(u), using the identity: tan²(x) + 1 = sec²(x)
= RHS