Trigonometry
- If 7 sin²θ+ 3 cos²θ= 4 (0° ≤ θ ≤ 90°), then value of θ is
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7 sin²θ + 3 cos²θ = 4
⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
⇒ 7 sin²θ + 3 – 3 sin²θ = 4
⇒ 4 sin²θ = 4 – 3 = 1⇒ sin²θ = 1 4 ⇒ sinθ = 1 = sin π 2 6 
⇒ θ = π 6
Correct Option: C
7 sin²θ + 3 cos²θ = 4
⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
⇒ 7 sin²θ + 3 – 3 sin²θ = 4
⇒ 4 sin²θ = 4 – 3 = 1⇒ sin²θ = 1 4 ⇒ sinθ = 1 = sin π 2 6 ⇒ θ = π 6
- If 7 sin²θ+ 3 cos²θ= 4 (0° ≤ θ ≤ 90°), then value of θ is
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View Hint View Answer Discuss in Forum
7 sin²θ + 3 cos²θ = 4
⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
⇒ 7 sin²θ + 3 – 3 sin²θ = 4
⇒ 4 sin²θ = 4 – 3 = 1⇒ sin²θ = 1 4 ⇒ sinθ = 1 = sin π 2 6 ⇒ θ = π 6
Correct Option: C
7 sin²θ + 3 cos²θ = 4
⇒ 7 sin²θ + 3 (1 – sin²θ) = 4
⇒ 7 sin²θ + 3 – 3 sin²θ = 4
⇒ 4 sin²θ = 4 – 3 = 1⇒ sin²θ = 1 4 ⇒ sinθ = 1 = sin π 2 6 ⇒ θ = π 6
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If tan 
π - θ 
= √3, the value of cosθ is : 2 2
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tan π - θ = √3 2 2 ⇒ cot θ = √3 = cot30° 2 ⇒ θ = 30° ⇒ θ = 60° 2 ∴ cos θ = cos 60° = 1 2
Correct Option: C
tan π - θ = √3 2 2 ⇒ cot θ = √3 = cot30° 2 ⇒ θ = 30° ⇒ θ = 60° 2 ∴ cos θ = cos 60° = 1 2
- If sec (7θ + 28°) = cosec (30° – 3θ) then the value of θ is
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sec (7θ + 28°)
= cosec (30° – 3θ)
⇒ sec (7θ + 28°)
= sec (90° – (30° –3θ))
⇒ 7θ + 28° = 90° – 30° + 3θ
⇒ 4θ = 90° – 30° – 28° = 32°⇒ θ = 32° = 8° 4
Correct Option: A
sec (7θ + 28°)
= cosec (30° – 3θ)
⇒ sec (7θ + 28°)
= sec (90° – (30° –3θ))
⇒ 7θ + 28° = 90° – 30° + 3θ
⇒ 4θ = 90° – 30° – 28° = 32°⇒ θ = 32° = 8° 4
- The value of (tan35° tan45° tan55°) is
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tan 35° . tan 45° . tan 55°
= tan 35° . 1 . tan (90° – 35°)
= tan 35° . 1 . cot 35° = 1.1 = 1
[tan (90° – θ) = cot θ ; tan θ . cot θ = 1]Correct Option: D
tan 35° . tan 45° . tan 55°
= tan 35° . 1 . tan (90° – 35°)
= tan 35° . 1 . cot 35° = 1.1 = 1
[tan (90° – θ) = cot θ ; tan θ . cot θ = 1]
