Verifying Trigonometric Identities

​5.1 Verifying Trigonometric Identities

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Multiple Select

Select all that are Pythagorean Identities. #36

• 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)

Multiple Choice

#1

• sin²θ

• cosθ

• tanθ

• 1- sin²θ

Multiple Choice

#2

• -1

• sin θ

• csc θ

• 1

Multiple Choice

#6

• csc s

• tan s + 1

• cot s

• cot s + 1

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Multiple Choice

Which expression is equivalent to the trigonometric expression $$\frac{1}{\left(1-\cos\left(\theta\right)\right)\cdot\left(1+\cos\left(\theta\right)\right)}$$  ? #24

• $$\sin^2\left(\theta\right)$$  

• $$\cos^2\left(\theta\right)$$  

• $$\sec^2\left(\theta\right)$$  

• $$\csc^2\left(\theta\right)$$  

Multiple Choice

$$\frac{1}{1-\sin x}+\frac{1}{1+\sin x}=$$  #42

• $$2\csc^2x$$  

• $$2\sec^2x$$  

• $$2\sin^2x$$  

• $$2\cos^2x$$  

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#3

• csc²θ

• sec²θ

• cscθ

• 1

Multiple Choice

#4

• sinθ

• cot²θ

• tan²θ

• cos²θ

Multiple Choice

#8

• sinθ

• cos²θ

• sin²θ

• 1- sin²θ

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Multiple Choice

Which expression is equivalent to the trigonometric expression $$\sin\left(\theta\right)\cdot\cot^2\left(\theta\right)\cdot\sec^2\left(\theta\right)$$  ? #27

• $$\sin\left(\theta\right)$$  

• $$\sec\left(\theta\right)$$  

• $$\csc\left(\theta\right)$$  

• $$\tan\left(\theta\right)$$  

Multiple Choice

Which expression is equivalent to the trigonometric expression $$\csc^2\left(\theta\right)-\cot^2\left(\theta\right)+\tan^2\left(\theta\right)$$  ? #28

• $$\sec^2\left(\theta\right)$$  

• $$\sec\left(\theta\right)$$  

• $$\csc\left(\theta\right)$$  

• $$\csc^2\left(\theta\right)$$  

Multiple Choice

Simplify the expression  $$\frac{\cot x}{\sec^2x+\csc^2x}$$  . #39

• $$\frac{\sin x\cos^2x}{\sec x}$$  

• $$\cos x\sin x$$  

• $$\frac{1}{\cot x+\sec x}$$  

• $$\sin x+\cos^3x$$  

Multiple Choice

Describe the first two steps of this proof. #37

• 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

Multiple Choice

What method would I use next to simplify the following: $$\frac{\tan x}{\sin x\cos x}-\frac{\cot x}{\sin x\cos x}$$  #41

• Substitution (Pythagorean Identities)

• Common Denominators

• Conjugate

• Express in Terms of Sine and Cosine