Step 3: Substitute sin(θ) into the identity: (1/√2)² + cos²(θ) = 1.
Step 4: Calculate (1/√2)²: (1/√2)² = 1/2.
Step 5: Now the equation looks like this: 1/2 + cos²(θ) = 1.
Step 6: To find cos²(θ), subtract 1/2 from both sides: cos²(θ) = 1 - 1/2.
Step 7: Calculate 1 - 1/2: 1 - 1/2 = 1/2.
Step 8: Now we have cos²(θ) = 1/2.
Step 9: To find cos(θ), take the square root of both sides: cos(θ) = √(1/2).
Step 10: Simplify √(1/2): √(1/2) = √2/2.
Trigonometric Identities – The question tests the understanding of the Pythagorean identity sin²(θ) + cos²(θ) = 1, which relates sine and cosine values.
Values of Trigonometric Functions – It assesses the knowledge of specific sine and cosine values, particularly for common angles.
