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Answers
Answer:
4) Option (a) => 87/25
5) Option (a) => 0
6) Option (a) => 1
7) Option (a) => 90°
Solution:
4)Here we go ↓
sin0°•sin1°•sin2°•....•sin88°•sin89°•sin90°
= sin0°(sin1°•sin2°•...•sin88°•sin89°•sin90°)
= 0•(sin1°•sin2°•...•sin88°•sin89°•sin90°)
= 0
Hence,
Required answer is 0
5) Here we go ↓
We have ;
=> 3sinθ = 4cosθ
=> sinθ / cosθ = 4/3
=> tanθ = 4/3 = p/b
Here,
p = 4 , b = 3
Now,
Using Pythagoras theorem , we have ;
=> h² = p² + b²
=> h² = 4² + 3²
=> h² = 16 + 9
=> h² = 25
=> h = √25
=> h = 5
Thus,
sinθ = p/h = 4/5
cosθ = b/h = 3/5
Thus,
4sin²θ - 3cos²θ + 2
= 4•(4/5)² - 3•(3/5)² + 2
= 4•(16/25) - 3•(9/25) + 2
= 64/25 - 27/25 + 2
= (64 - 27)/25 + 2
= 37/25 + 2
= (37 + 50)/25
= 87/25
Hence,
Required answer is 87/25
6) Here we go ↓
We have ;
=> cos9α = sinα
=> cos9α = cos(90° - α)
=> 9α = 90° - α
=> 9α + α = 90°
=> 10α = 90°
=> α = 90°/10
=> α = 9°
Thus,
tan5α = tan(5×9°) = tan45° = 1
Hence,
Required value of tan5α is 1 .
7) Here we go ↓
We have ;
=> 2sin²θ - cos²θ = 2
=> 2sin²θ - (1 - sin²θ) = 2
=> 2sin²θ - 1 + sin²θ = 2
=> 3sin²θ = 2 + 1
=> 3sin²θ = 3
=> sin²θ = 3/3
=> sin²θ = 1
=> sinθ = √1
=> sinθ = 1
=> sinθ = sin90°
=> θ = 90°
Hence,
The required value of θ is 90°