IIT Level Trigonometry – 100 Questions (Set 1: 1–20)

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1. sinθ + cosθ = √2 అయితే sinθcosθ = ?
Step 1: Square both sides
( sinθ + cosθ )² = 2
Step 2: 1 + 2sinθcosθ = 2
Step 3: sinθcosθ = 1/2
Answer = 1/2

2. sinθ + cosθ = 1 అయితే sinθcosθ = ?
Step: 1 + 2sinθcosθ = 1
sinθcosθ = 0
Answer = 0

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

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

5. sinθ + cosθ max value?
Answer = √2

6. tanθ + cotθ min value?
Step: ≥ 2
Answer = 2

7. tanθ + cotθ = 2 అయితే θ = ?
Step: tanθ = 1
Answer = 45°

8. sinθcosθ = 1/4 అయితే (sinθ + cosθ)² = ?
Step: = 1 + 2(1/4)
Answer = 3/2

9. sin⁴θ + cos⁴θ = ?
Step: = 1 − 2sin²θcos²θ
Answer = 1 − 2sin²θcos²θ

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

11. sinθ + cosθ = a అయితే sinθcosθ = ?
Answer = (a² − 1)/2

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

13. sinθ + cosθ = √2 అయితే sin³θ + cos³θ = ?
Step: = √2/2
Answer = √2/2

14. sinθcosθ = 1/2 అయితే sin³θcos³θ = ?
Answer = 1/8

15. tanθ = 3 అయితే sinθcosθ = ?
Step: = tanθ / (1 + tan²θ)
= 3/10
Answer = 3/10

16. tanθ = a అయితే sinθcosθ = ?
Answer = a/(1+a²)

17. sin²θcos²θ max value?
Answer = 1/4

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

19. sinθcosθ ≤ ?
Answer = 1/2

20. sinθ + cosθ = 2 అయితే possible?
Answer = Not possible

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