Question

Express cos∅ in terms of cot∅.

Answer 1

Hey mate☺

See the attachment.

I hope it helps you ☺✌✌

Answer 2

SOLUTION

Consider,

$= > tan \theta = \frac{1}{cot \theta} \\ = > tan {}^{2} \theta = \frac{1}{ {cot}^{2} \theta } = {sec}^{2} \theta - 1 = \frac{1}{ {cot}^{2} \theta} \\ = > {sec}^{2} \theta = \frac{1}{ {cot}^{2} \theta} + 1 = {sec}^{2} \theta = \frac{1 + {cot}^{2} \theta }{ {cot}^{2} \theta} \\ \\ = > sec \theta = \sqrt{ \frac{1 + {cot}^{2} \theta }{ {cot}^{2} \theta} } = \frac{1}{cos \theta} = \sqrt{ \frac{1 + {cot}^{2} \theta }{cot {}^{2} \theta } } \\ \\ = > cos \theta = \sqrt{ \frac{cot {}^{2} \theta }{1 + {cot}^{2} \theta } } = \frac{cot \theta}{ \sqrt{1 + {cot}^{2} \theta } } \\ = > cos \theta = \frac{cot \theta}{ \sqrt{1 + {cot}^{2} \theta} }$