Let us consider a right triangle ABC, right-angled at point B

Cot =

= If BC is 7k, then AB will be 8k, where k is a positive integer.

Applying Pythagoras theorem in ΔABC, we obtain

AC² = AB² + BC²

= (8k)² + (7k)²

= 64k² + 49k²

= 113k²

AC = k

Sin =

=

=

Cos θ =

=

=

(i) = (1 – sin² θ)/(1 – cos² θ)

=

=

=

(ii) Cot² θ = (cot θ)²

= (² =