Trigonometry

sin 45° = 1/√2, cos 60° = 1/2, sin 90° = 1

From standard trigonometric values: sin 45° = 1/√2 ✓, cos 60° = 1/2 ✓, sin 90° = 1 ✓. However, tan 30° = 1/√3 (not √3), and cos 0° = 1 (not 0).

2/√2

Step 1: cos 45° = 1/√2 and sin 45° = 1/√2. Step 2: cos 45° + sin 45° = 1/√2 + 1/√2 = 2/√2 = √2.

45°

Step 1: We know sin θ = cos θ. Step 2: From complementary angle relation, sin θ = cos(90° - θ). Step 3: So cos θ = cos(90° - θ), which means θ = 90° - θ. Step 4: Solving: 2θ = 90°, therefore θ = 45°.

sin θ = cos(90° - θ), cos θ = sin(90° - θ), tan θ = cot(90° - θ)

For complementary angles: sin θ = cos(90° - θ) ✓, cos θ = sin(90° - θ) ✓, tan θ = cot(90° - θ) ✓. The incorrect options show equal ratios which only occur at 45°.