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AssignmentMultiple Select

Trigonometric Sum Identities

Question 1 • Precalculus

Which expressions are equivalent to cos2(105°) – sin2(105°)? Check all that apply.1 – 2sin2(105°)2cos2(105°) – 12sin(105°) cos(105°)cos(105°)cos(210°)

Answer
A
1 – 2sin2(105°)
B
2cos2(105°) – 1
C
2sin(105°) cos(105°)
D
cos(105°)
E
cos(210°)

Explanation

Use the double-angle identities: cos²θ − sin²θ = 1 − 2sin²θ = 2cos²θ − 1 = cos(2θ). With θ = 105°, these expressions are 1 − 2sin²(105°), 2cos²(105°) − 1, and cos(210°), so choices A, B, and E are equivalent. Choice C equals sin(210°), not cos(210°).

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