Answer:
Based on two Pythagorean Identities:
- 1 + tan²θ = sec²θ
- 1 + cot²θ = csc²θ
sec²θ(1 - cot²θ)
= sec²θ - sec²θ · cot²θ
[tex]=\frac{1}{cos ^{2} \theta} -\frac{1}{cos ^{2}\theta }*\frac{cos ^{2}\theta}{sin^{2} \theta}\\\\=\frac{1}{cos ^{2}\theta }-\frac{1}{sin^{2}\theta }\\\\=sec^{2}\theta-csc^{2}\theta\\\\=1+tan^{2}\theta-(1+cot^{2}\theta)\\\\=1+tan^{2}\theta-1-cot^{2}\theta\\\\=tan^{2}\theta-cot^{2}\theta[/tex]
