IIT Level Trigonometry – 100 Questions (Set 2: 21–40)

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21. sinθ − cosθ = 0 అయితే sinθcosθ = ?
Step: θ = 45° → sinθcosθ = 1/2
Answer = 1/2

22. sinθ + cosθ = 0 అయితే sinθcosθ = ?
Step: θ = 135° → sinθcosθ = −1/2
Answer = −1/2

23. sin²θ − cos²θ = 0 అయితే θ = ?
Step: sin²θ = cos²θ → θ = 45°
Answer = 45°

24. sinθcosθ = 1/3 అయితే (sinθ + cosθ)² = ?
Step: = 1 + 2/3
Answer = 5/3

25. sinθcosθ = a అయితే sin⁴θ + cos⁴θ = ?
Answer = 1 − 2a²

26. sinθ + cosθ = a అయితే sin⁴θ + cos⁴θ = ?
Step: sinθcosθ = (a²−1)/2
= 1 − (a²−1)²/2
Answer = 1 − (a²−1)²/2

27. tanθ + cotθ = 3 అయితే sinθcosθ = ?
Step: = 1/3
Answer = 1/3

28. tanθ + cotθ = a అయితే sinθcosθ = ?
Answer = 1/a

29. sinθcosθ = a అయితే tanθ + cotθ = ?
Answer = 1/a

30. tanθ = 2 అయితే sinθcosθ = ?
Step: = 2/(1+4)
Answer = 2/5

31. tanθ = 1 అయితే sin²θcos²θ = ?
Step: (1/2)²
Answer = 1/4

32. sinθ + cosθ = √2 అయితే sin²θcos²θ = ?
Answer = 1/4

33. sinθ + cosθ = 1 అయితే sin²θcos²θ = ?
Answer = 0

34. sinθcosθ = a అయితే sin⁶θ + cos⁶θ = ?
Answer = 1 − 3a²

35. sinθ + cosθ = a అయితే sin⁶θ + cos⁶θ = ?
Answer = 1 − 3[(a²−1)/2]²

36. sinθ = 3/5 అయితే cosθ = ?
Answer = 4/5

37. cosθ = 5/13 అయితే sinθ = ?
Answer = 12/13

38. tanθ = 4/3 అయితే sinθ = ?
Answer = 4/5

39. tanθ = 5 అయితే sinθcosθ = ?
Answer = 5/26

40. tanθ + cotθ min value?
Answer = 2

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