If evaluate:

(i)

(ii)

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

AC^{2} = AB^{2} + BC^{2}

= (8k)^{2} + (7k)^{2}

= 64k^{2} + 49k^{2}

= 113k^{2}

AC = k

Sin =

=

=

Cos θ =

=

=

(i) = (1 – sin^{2} θ)/(1 – cos^{2} θ)

=

=

=

(ii) Cot^{2} θ = (cot θ)^{2}

= (^{2} =

10