Question

Which identity/formula was used to simplify from step 2 to step 3?

Answer 1

The reciprocal identities of trigonometry include the identities below

`\begin{gathered} \csc \theta=(1)/(\sin \theta) \\ \sec \theta=(1)/(\cos \theta) \\ \cot \theta=(1)/(\tan \theta) \\ \tan \theta=(1)/(\cot \theta) \\ \cos \theta=(1)/(\sec \theta) \\ \sin \theta=(1)/(\csc \theta) \end{gathered}`

The quotient identity include the identities below

`\begin{gathered} \tan \theta=(\sin \theta)/(\cos \theta) \\ \cot \theta=(\cos \theta)/(\sin \theta) \end{gathered}`

The sum formula of trigonometric identity include

`\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}`

The double-angle formula is given below as

Hence,

The final answer is QUOTIENT IDENTITY