Reciprocal Identities

Reference > Algebra: Trigonometric Identities

Description

\(\sin{x}=\frac{1}{\csc{x}}\)

\(\cos{x}=\frac{1}{\sec{x}}\)

\(\tan{x}=\frac{1}{\cot{x}}\)

\(\csc{x}=\frac{1}{\sin{x}}\)

\(\sec{x}=\frac{1}{\cos{x}}\)

\(\cot{x}=\frac{1}{\tan{x}}\)


Examples

Example 1

\[\sec{(2y)}-\frac{1}{\cos{(2y)}}\]
1
Use this property: \(\cos{x}=\frac{1}{\sec{x}}\).
\[\sec{2y}-\sec{2y}\]

2
Simplify.
\[0\]

Done


 

Example 2

\[\frac{4}{\csc{x}}+\sin{x}\]
1
Simplify  \(\frac{4}{\csc{x}}\)  to  \(4\sin{x}\).
\[4\sin{x}+\sin{x}\]

2
Simplify.
\[5\sin{x}\]

Done


 
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