Prove the following identities using the application of reciprocal and quotient relations.

(a) [tex]\tan \theta \cdot \cot \theta = 1[/tex]

(b) [tex]\cos \theta \cdot \sec \theta = 1[/tex]

(c) [tex]\operatorname{cosec} \theta \cdot \sin \theta = 1[/tex]

(d) [tex]\operatorname{cosec} A \cdot \tan A \cdot \cos A = 1[/tex]

(e) [tex]\sin A \cdot \cot A \cdot \sec A = 1[/tex]

(f) [tex]\frac{\sin A \cdot \sec A}{\operatorname{cosec} A \cdot \cos A} = \tan^2 A[/tex]

(g) [tex]\frac{\cos A}{\cot A} = \sin A[/tex]

(h) [tex]\frac{\operatorname{cosec} \alpha}{\cot \alpha} = \sec \alpha[/tex]

(i) [tex]\frac{\cos \theta}{\tan \theta \cdot \cot^2 \theta} = \sin \theta[/tex]

(j) [tex]\frac{\sin \theta \cdot \sec \theta}{\operatorname{cosec} \theta \cdot \cos \theta} = \tan^2 \theta[/tex]

(k) [tex]\frac{\operatorname{cosec} \theta \cdot \tan \theta}{\sec^2 \theta} = \cos \theta[/tex]

(l) [tex]\frac{\tan \theta \cdot \cot \theta}{\sec \theta \cdot \operatorname{cosec} \theta} = \sin \theta \cdot \cos \theta[/tex]