If A = tanθ, B = secθ, C = sinθ and D = cosθ, then the value of A² − B² + 2CD is

A² − B² + 2CD = tan²θ − sec²θ + 2sinθcosθ

= −(sec²θ − tan²θ − 2sinθcosθ) 

= −(1 − 2 sinθcosθ)

= −(sin²θ + cos²θ − 2sinθcosθ) 

= −(sinθ − cosθ)² 

= − (C − D)²