Reciprocal Identities

Reference > Algebra: Trigonometric Identities

Description

sin⁡x=1csc⁡x\sin{x}=\frac{1}{\csc{x}}

cos⁡x=1sec⁡x\cos{x}=\frac{1}{\sec{x}}

tan⁡x=1cot⁡x\tan{x}=\frac{1}{\cot{x}}

csc⁡x=1sin⁡x\csc{x}=\frac{1}{\sin{x}}

sec⁡x=1cos⁡x\sec{x}=\frac{1}{\cos{x}}

cot⁡x=1tan⁡x\cot{x}=\frac{1}{\tan{x}}


Examples

Example 1

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

2
Simplify.
00

Done


 

Example 2

4csc⁡x+sin⁡x\frac{4}{\csc{x}}+\sin{x}
1
Simplify  4csc⁡x\frac{4}{\csc{x}}  to  4sin⁡x4\sin{x}.
4sin⁡x+sin⁡x4\sin{x}+\sin{x}

2
Simplify.
5sin⁡x5\sin{x}

Done


 
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