Trigonometric Identity Proofs Worksheet
Prove trigonometric identities using fundamental identities and algebraic manipulation.
Includes
2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False
Standards
CCSS.MATH.CONTENT.HSG.SRT.C.8CCSS.MATH.CONTENT.HSF.TF.C.8
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Trigonometric Identity Proofs
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Prove each of the following trigonometric identities. Show all your work clearly and logically.
1. Prove the identity: (sin x + cos x)² = 1 + 2 sin x cos x
2. Prove the identity: tan x + cot x = sec x csc x
3. To prove identities, we often start by rewriting all expressions in terms of and .
4. The Pythagorean identity states that sin²θ + cos²θ = .
5. Which of the following is equivalent to (1 - sin²θ) / cos θ?
a
sin θ
b
cos θ
c
tan θ
d
sec θ
6. The identity 1 + tan²θ = sec²θ is a Pythagorean identity.
T
True
F
False