ట్రిగోనమెట్రీ – Step-wise Solved Problems (41–60)

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41. (sinθ + cosθ)² + (sinθ − cosθ)² = ?
Step 1: Expand both
= (1 + 2sinθcosθ) + (1 − 2sinθcosθ)
Step 2: Add → 2
Answer = 2

42. sin⁴θ + cos⁴θ = ?
Step 1: = (sin²θ + cos²θ)² − 2sin²θcos²θ
Step 2: = 1 − 2sin²θcos²θ
Answer = 1 − 2sin²θcos²θ

43. sinθcosθ max value?
Step: occurs at θ = 45°
Answer = 1/2

44. sinθ + cosθ max value?
Answer = √2

45. sinθ + cosθ = 1 అయితే sinθcosθ = ?
Step 1: Square both sides
Step 2: 1 + 2sinθcosθ = 1
Step 3: sinθcosθ = 0
Answer = 0

46. sinθcosθ = 1/2 అయితే sinθ + cosθ = ?
Step: occurs at 45°
Answer = √2

47. sin²θ − cos²θ = ?
Answer = −cos2θ

48. 1 + tan²θ = ?
Answer = sec²θ

49. 1 + cot²θ = ?
Answer = cosec²θ

50. tanθ × cotθ = ?
Answer = 1

51. sinθ / cosθ = tanθ నిరూపించండి
Step: Definition apply
Answer = tanθ

52. cosθ / sinθ = cotθ నిరూపించండి
Answer = cotθ

53. secθ × cosθ = ?
Step: (1/cosθ) × cosθ
Answer = 1

54. cosecθ × sinθ = ?
Answer = 1

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

56. cosθ − sinθ max value?
Answer = √2

57. tanθ period?
Answer = π

58. sinθ period?
Answer = 2π

59. cosθ period?
Answer = 2π

60. tanθ undefined value?
Answer = 90°

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Shaktimatha Learning | Step-wise Practice Series