(tanθ + cotθ)² = sec²θ + csc²θ
Expand left side: tan²θ + 2tanθcotθ + cot²θ
Evaluate middle term: 2tanθcotθ = [tex]2*\frac{sin\theta}{cos\theta}*\frac{cos\theta}{sin\theta}[/tex] = 2
⇒ tan²θ + 2+ cot²θ
= tan²θ + 1 + 1 + cot²θ
Apply trig identity: tan²θ + 1 = sec²θ
⇒ sec²θ + 1 + cot²θ
Apply trig identity: 1 + cot²θ = csc²θ
⇒ sec²θ + csc²θ
Left side equals Right side so equation is verified
