Pythagorean Identities

Reference > Algebra: Trigonometric Identities

Description

\({sin}^{2}x+{cos}^{2}x=1\)

\({tan}^{2}x+1={sec}^{2}x\)

\({cot}^{2}x+1={csc}^{2}x\)


Examples

Example 1 [Top]

\[{sin}^{2}x+4x+{cos}^{2}x\]
1
Use Pythagorean Identities: \({sin}^{2}x+{cos}^{2}x=1\)
\[4x+1\]

Done


 

Example 2 [Top]

\[\frac{{cos}^{2}2y-2y+{sin}^{2}2y-1}{4}\]
1
Use Pythagorean Identities: \({sin}^{2}x+{cos}^{2}x=1\)
\[\frac{-2y-1+1}{4}\]

2
Simplify \(-2y-1+1\) to \(-2y\)
\[\frac{-2y}{4}\]

3
Move the negative sign to the left
\[-\frac{2y}{4}\]

4
Simplify \(\frac{2y}{4}\) to \(\frac{y}{2}\)
\[-\frac{y}{2}\]

Done