Trigonometry

sin 30° = 1/2, cos 60° = 1/2, sin 90° = 1, cos 0° = 1

sin 30° = 1/2 ✓, cos 60° = 1/2 ✓, tan 30° = 1/√3 (not √3) ✗, sin 90° = 1 ✓, cos 0° = 1 ✓. These are standard values from the trigonometric table.

sec²θ

This is one of the fundamental trigonometric identities: 1 + tan²θ = sec²θ. It can be derived by dividing the identity sin²θ + cos²θ = 1 by cos²θ.

1

sin 45° = cos 45° = 1/√2. So sin²45° + cos²45° = (1/√2)² + (1/√2)² = 1/2 + 1/2 = 1. This also follows from the identity sin²θ + cos²θ = 1.

cos θ/sin θ, 1/tan θ, adjacent/opposite

cot θ = cos θ/sin θ ✓, cot θ = 1/tan θ ✓, cot θ = adjacent/opposite ✓. The expressions opposite/adjacent and sin θ/cos θ are equal to tan θ, not cot θ.