Solution:
The reciprocal identities of trigonometry include the identities below
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \sec \theta=\frac{1}{\cos \theta} \\ \cot \theta=\frac{1}{\tan \theta} \\ \tan \theta=\frac{1}{\cot \theta} \\ \cos \theta=\frac{1}{\sec \theta} \\ \sin \theta=\frac{1}{\csc \theta} \end{gathered}[/tex]
The quotient identity include the identities below
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \cot \theta=\frac{\cos \theta}{\sin \theta} \end{gathered}[/tex]
The sum formula of trigonometric identity include
[tex]\begin{gathered} \sin (\alpha+\beta)=\sin \alpha\cos \beta+\cos \alpha\sin \beta \\ \sin (\alpha-\beta)=\sin \alpha\cos \beta-\cos \alpha\sin \beta \\ \cos (\alpha+\beta)=\cos \alpha\cos \beta-\sin \alpha\sin \beta \\ \cos (\alpha-\beta)=\cos \alpha\cos \beta+\sin \alpha\sin \beta \end{gathered}[/tex]
The double-angle formula is given below as
Hence,
The final answer is QUOTIENT IDENTITY
