Pythagorean Identities

Reference > Algebra: Trigonometric Identities

Description

sin⁡2x+cos⁡2x=1\sin^{2}x+\cos^{2}x=1

tan⁡2x+1=sec⁡2x\tan^{2}x+1=\sec^{2}x

cot⁡2x+1=csc⁡2x\cot^{2}x+1=\csc^{2}x


Examples

Example 1

sin⁡2x+4x+cos⁡2x\sin^{2}x+4x+\cos^{2}x
1
Use Pythagorean Identities: sin⁡2x+cos⁡2x=1\sin^{2}x+\cos^{2}x=1.
4x+14x+1

Done


 

Example 2

cos⁡22y−2y+sin⁡22y−14\frac{\cos^{2}2y-2y+\sin^{2}2y-1}{4}
1
Use Pythagorean Identities: sin⁡2x+cos⁡2x=1\sin^{2}x+\cos^{2}x=1.
−2y−1+14\frac{-2y-1+1}{4}

2
Simplify  −2y−1+1-2y-1+1  to  −2y-2y.
−2y4\frac{-2y}{4}

3
Move the negative sign to the left.
−2y4-\frac{2y}{4}

4
Simplify  2y4\frac{2y}{4}  to  y2\frac{y}{2}.
−y2-\frac{y}{2}

Done


 
Cymath foriOSAndroid