RRB Group D Complementary Angles

Identify complementary angles. Since 30° + 60° = 90°, these are complementary.

Apply complementary relationships. cos 60° = cos(90° - 30°) = sin 30°, sin 60° = sin(90° - 30°) = cos 30°.

Substitute values. sin 30° × sin 30° + cos 30° × cos 30° = (sin 30°)² + (cos 30°)².

Use standard values. sin 30° = 1/2, cos 30° = √3/2.

Calculate final answer. (1/2)² + (√3/2)² = 1/4 + 3/4 = 1. Another shortcut involves recognizing patterns. Expression like sin²θ + cos²θ always equals 1. When you see complementary angles multiplied or added in specific patterns, look for these standard identities. Common mistakes include forgetting that complementary means sum equals 90°, not 180°. Students often confuse complementary with supplementary angles. Another error is applying relationships incorrectly - remember sin(90° - θ) = cos θ, not sin θ = cos(90° - θ)