1. x + y = sin²θ + cos²θ + 1 = 1 + 1 = 2
2. k = sec²θ(1 - sin²θ) = sec²θ * cos²θ = 1
3. sin20°sin70° - cos20°cos70° = -cos(20°+70°) = -cos90° = 0
4. tanθ * 1 = 1 → tanθ = 1 → θ = 45°
5. sin²10° + sin²80° = sin²10° + cos²10° = 1
6. tan²A - sec²A = (sin²A/cos²A) - (1/cos²A) = (sin²A - 1)/cos²A = -cos²A/cos²A = -1
7. sin2A = cos3A → sin2A = sin(90°-3A) → 2A = 90°-3A → 5A = 90° → A = 18°
8. tanθ - cotθ = 0 → tanθ = cotθ → tanθ = 1/tanθ → tan²θ = 1 → tanθ = ±1 → θ = 45° or 135°, etc. (Principal value: 45°)
9. smaller
10. Area = (1/2)*AB*BC. Since ∠ACB=45° and ∠ABC=90°, AB = BC = 8cm. Area = (1/2)*8*8 = 32 cm²
11. In Fig. 2 (left), the angle of depression is ∠QPR. In Fig. 2 (right), the angle of depression is ∠ABC.
Parent Tip: Review the logic above to help your child master the concept of trigonometry worksheet grade 10.
