If cot(2θ + 25°) = tan(θ + 20°), then find cot3θ + sec3θ.

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B√2

C1 + √2

Answer:

cot(2θ + 25°) = tan(θ + 20°) cot(2θ + 25°) = cot(90° -(θ + 20°) 2θ + 25° = 90° - (θ + 20°) 3θ = 45° θ = 15° cot3θ + sec3θ = cot45° + sec45° = 1 + √2

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