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