Verifying Trigonometric Identities

sin²(u) + cos²(u) = 1

sin²(u) - cos²(u) = 1

tan²(u) + 1 = sec²(u)

cot²(u) + csc²(u) = 1

cot²(u) + 1 = csc²(u)

sin²θ

cosθ

tanθ

1- sin²θ

-1

sin θ

csc θ

1

csc s

tan s + 1

cot s

cot s + 1

$$\sin^2\left(\theta\right)$$  

$$\cos^2\left(\theta\right)$$  

$$\sec^2\left(\theta\right)$$  

$$\csc^2\left(\theta\right)$$  

$$2\csc^2x$$  

$$2\sec^2x$$  

$$2\sin^2x$$  

$$2\cos^2x$$  

csc²θ

sec²θ

cscθ

1

sinθ

cot²θ

tan²θ

cos²θ

sinθ

cos²θ

sin²θ

1- sin²θ

$$\sin\left(\theta\right)$$  

$$\sec\left(\theta\right)$$  

$$\csc\left(\theta\right)$$  

$$\tan\left(\theta\right)$$  

$$\sec^2\left(\theta\right)$$  

$$\sec\left(\theta\right)$$  

$$\csc\left(\theta\right)$$  

$$\csc^2\left(\theta\right)$$  

$$\frac{\sin x\cos^2x}{\sec x}$$  

$$\cos x\sin x$$  

$$\frac{1}{\cot x+\sec x}$$  

$$\sin x+\cos^3x$$  

1: Find a common denominator to combine the fractions.

2: Combine the fractions.

1: Separate the fraction

2: multiply by conjugate

1: Change to sines and cosines

2: Combine fractions

1:Square both sides

2: Cancel common factors

Substitution (Pythagorean Identities)

Common Denominators

Conjugate

Express in Terms of Sine and Cosine