Check my answers. images below for both

4. It can be helpful to consider the identities related to each of the answer choices.
• cot(θ) = 1/tan(θ) . . . . 1/tan(θ) + tan(θ) ≢ 1

• sec(θ) = 1/cos(θ), csc(θ)=1/sin(θ) . . . . 1/cos(θ)² + 1/sin(θ)² =
    (sin(θ)²+cos(θ)²)/(sin(θ)²cos(θ)²) = 1/(sin(θ)²cos(θ)²) ≢ 1

• sec(θ) = 1/cos(θ), tan(θ) = sin(θ)/cos(θ) . . . . (sin(θ)/cos(θ))² ≡ sin(θ)²×1/cos(θ)²
  tan(θ)² = sin(θ)²×sec(θ)² is the correct choice

• sec(θ) = 1/cos(θ), tan(θ) = sin(θ)/cos(θ) . . . . cos(θ)² ≠ 1/cos(θ)²×(sin(θ)/cos(θ))²

1. cot(290°) = -tan(20°) ≈ -0.36
  The second selection is a better choice.

#4 should be the third choice.
#1 is -0.36 .