ట్రిగోనమెట్రీ – Step-wise Solved Problems (21–40)

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21. sin 60° + cos 30° = ?
Step 1: sin60° = √3/2
Step 2: cos30° = √3/2
Step 3: Add → √3
Answer = √3

22. tan 60° × tan 30° = ?
Step 1: tan60° = √3
Step 2: tan30° = 1/√3
Step 3: Multiply → 1
Answer = 1

23. sin²45° + cos²45° = ?
Step 1: Identity apply
Answer = 1

24. sinθ / cosθ = ?
Step: tanθ
Answer = tanθ

25. (sinθ + cosθ)² = ?
Step 1: Formula apply
Step 2: = sin²θ + cos²θ + 2sinθcosθ
Step 3: = 1 + 2sinθcosθ
Answer = 1 + 2sinθcosθ

26. (sinθ − cosθ)² = ?
Step: = 1 − 2sinθcosθ
Answer = 1 − 2sinθcosθ

27. sinθ + cosθ = √2 అయితే θ = ?
Step: Max value occurs at 45°
Answer = 45°

28. sinθcosθ = 1/2 అయితే θ = ?
Step: Occurs at 45°
Answer = 45°

29. sin²30° + cos²60° = ?
Step 1: (1/2)² = 1/4
Step 2: (1/2)² = 1/4
Step 3: Add → 1/2
Answer = 1/2

30. tan²30° = ?
Step 1: tan30° = 1/√3
Step 2: square → 1/3
Answer = 1/3

31. sec 0° = ?
Step: 1/cos0° = 1
Answer = 1

32. cosec 90° = ?
Step: 1/sin90° = 1
Answer = 1

33. sinθ − cosθ = 0 అయితే θ = ?
Step: θ = 45°
Answer = 45°

34. tanθ = 1 అయితే θ = ?
Step: θ = 45°
Answer = 45°

35. sinθ = 1 అయితే θ = ?
Answer = 90°

36. cosθ = 0 అయితే θ = ?
Answer = 90°

37. tanθ = √3 అయితే θ = ?
Answer = 60°

38. sinθ = 1/2 అయితే θ = ?
Answer = 30°

39. cosθ = 1/2 అయితే θ = ?
Answer = 60°

40. sinθ + cosθ min value?
Answer = −√2

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Shaktimatha Learning | Step-wise Practice Series