Find sin²30° + cos²30°

sin30° = 1/2, cos30° = √3/2

= (1/2)² + (√3/2)²

= 1/4 + 3/4

= 1

Evaluate tan45° + cos60°

= 1 + 1/2

= 3/2

Find sec60°

secθ = 1/cosθ

= 1/(1/2)

= 2

Evaluate cosec30°

= 1/sin30°

= 1/(1/2)

= 2

Find tan30°

= 1/√3

Evaluate sin60° + cos30°

= √3/2 + √3/2

= √3

Find value of sin45° × cos45°

= (1/√2)(1/√2)

= 1/2

Evaluate tan45° × cot45°

= 1 × 1

= 1

Find cos²45°

= (1/√2)²

= 1/2

Evaluate sin90° − cos0°

= 1 − 1

= 0

Prove: sin²θ + cos²θ = 1

This is a fundamental trigonometric identity and holds true for all angles θ.

Evaluate (1 + tan²45°)

= 1 + 1²

= 2

Evaluate sec²30° − tan²30°

Using identity: sec²θ − tan²θ = 1

= 1

Evaluate (sin60° / cos60°)

= (√3/2)/(1/2)

= √3

Find value of tan30° × tan60°

= (1/√3)(√3)

= 1

A tower subtends an angle of 30° at a point on the ground. If distance from the tower is 20m, find height.

tan30° = h/20

1/√3 = h/20

h = 20/√3 ≈ 11.55m

Angle of elevation of a building is 45° and distance is 10m.

tan45° = h/10

1 = h/10

h = 10m

A ladder makes an angle of 60° with the ground and touches a wall at 5m height. Find ladder length.

sin60° = 5/L

L = 5/(√3/2)

L ≈ 5.77m

Question 19: Evaluate cos60° + sin30° = 1

Question 20: Find tan60° − tan30° = √3 − 1/√3

Question 21: Evaluate sin²45° + cos²45° = 1

Question 22: Find sec30° = 2/√3

Question 23: Evaluate cosec45° = √2

Question 24: Find tan²45° = 1

Question 25: Evaluate sin30° × cos60° = 1/4

Question 26: Find sin60° × cos30° = 3/4

Question 27: Evaluate tan45° + cot45° = 2

Question 28: Find sin²30° = 1/4

Question 29: Evaluate cos²60° = 1/4

Question 30: Find tan30° × tan60° = 1

Question 31: Evaluate sin90° + cos90° = 1

Question 32: Evaluate sin0° + cos0° = 1

Question 33: Find sec45° = √2

Question 34: Evaluate cosec60° = 2/√3

Question 35: Find tan0° = 0

Question 36: Evaluate cos90° = 0

Question 37: Find sin0° = 0

Question 38: Evaluate tan90° (undefined)

Question 39: Find cos45° = 1/√2

Question 40: Evaluate sin45° = 1/√2

Question 41: Evaluate tan60° = √3

Question 42: Find sin30° = 1/2

Question 43: Evaluate cos30° = √3/2

Question 44: Evaluate tan30° = 1/√3

Question 45: Evaluate cot30° = √3

Question 46: Evaluate sec60° = 2

Question 47: Evaluate cosec90° = 1

Question 48: Evaluate sin²60° + cos²60° = 1

Question 49: Evaluate tan²45° + 1 = sec²45°

Question 50: Verify identity: 1 + tan²θ = sec²θ