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Verify Trigonometric Identities by Algebraic Manipulation
Worksheet
Grade Level
Pre-Calculus
Pre-CAL.98 Verify Trigonometric Identities by Algebraic Manipulation
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🔴 Hard
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Verify the identity: (cos x − cos y)/(sin x + sin y) = −tan((x − y)/2). Which option shows a valid verification sequence?
A
cos x − cos y = 2cos((x+y)/2)cos((x−y)/2) and sin x + sin y = 2sin((x+y)/2)sin((x−y)/2), so the ratio is cot((x−y)/2)
B
cos x − cos y = −2sin((x+y)/2)sin((x−y)/2) and sin x + sin y = 2sin((x+y)/2)cos((x−y)/2), so the ratio is −tan((x−y)/2)
C
(cos x − cos y)/(sin x + sin y) ⇒ cos(x−y)/sin(x+y) ⇒ −tan((x−y)/2)
D
(cos x − cos y)/(sin x + sin y) ⇒ (cos x)/(sin x) − (cos y)/(sin y) ⇒ cot x − cot y
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