For any angle θ between 0° and 45°, cos²(45° + θ) + cos²(45° − θ) equals

1. 45^° - \θ = 90^° - (45^° + \θ), so (45^°-\θ) = (45^°+\θ) and the sum is ^2 + ^2 = 1.

For any angle θ between 0° and 45°, co $s^{2}$ (45° + θ) + co $s^{2}$ (45° − θ) equals

Competition practiceTrigonometry

4 5^{\circ} - θ = 9 0^{\circ} - (4 5^{\circ} + θ)

, so

cos (4 5^{\circ} - θ) = sin (4 5^{\circ} + θ)

and the sum is

cos^{2} + sin^{2} = 1

Answer: A) 1

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