\(\sin \theta:-\)
\(\sin \theta=\frac{1}{\operatorname{cosec} \theta}\)
\(\operatorname{Cos} \theta:-\)
\(\sin ^2 \theta+\cos ^2 \theta =1 \)
\(\cos ^2 \theta =1-\sin ^2 \theta \)
\(\cos \theta =\sqrt{1-\sin ^2 \theta} \)
\(\cos \theta =\sqrt{1-\left(\frac{1}{\operatorname{cosec} \theta}\right)^2} \)
\(\cos \theta =\sqrt{1-\frac{1}{\operatorname{cosec}^2 \theta}}\)
\(\tan \theta:-\)
\(\tan \theta =\frac{\sin \theta}{\cos \theta} \)
\(=\frac{\frac{1}{\operatorname{cosec} \theta}}{\sqrt{1-\frac{1}{\operatorname{cosec}^2 \theta}}} \)
\(=\frac{1}{\operatorname{cosec} \theta \sqrt{1-\frac{1}{\operatorname{cosec} \theta}}}\)
\(Cot\ \theta:-\)
\(\cot \theta =\frac{1}{\tan \theta} \)
\(=\frac{1}{\frac{1}{\operatorname{cosec} \theta \sqrt{1-\frac{1}{\operatorname{cosec} \theta}}}} \Rightarrow \operatorname{cosec} \theta \sqrt{1-\frac{1}{\operatorname{cosec}^2 \theta}} \)
\(\sec \theta =\frac{1}{\cos \theta} \)
\(=\frac{1}{\sqrt{1-\frac{1}{\operatorname{cose}^2 \theta}}}\)
