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

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

Done


 

Example 2

\[\frac{\cos^{2}2y-2y+\sin^{2}2y-1}{4}\]
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


 
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