If 7 – 2sin2θ – 11cosθ = 0, where 0° < θ < 90° then find the value of θ
1. 90°
2. 60°
3. 30°
4. 45°
1. 90°
2. 60°
3. 30°
4. 45°
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Correct Answer – Option 2 : 60°
Given:
Our given expression is 7 – 2sin2θ – 11cosθ = 0
Formula used:
cos2θ + sin2θ = 1
Calculation:
Our given expression is 7 – 2sin2θ – 11cosθ = 0
⇒ 7 – 2(1 – cos2θ) – 11cosθ = 0
⇒ 7 – 2 + 2cos2θ – 11cosθ = 0
Put cosθ = t, then our equation becomes
⇒ 2t2 – 11t + 5 = 0
⇒ (t – 5)(t – 1/2) = 0
⇒ t = 5 or t = ½
Here t = 5 is not possible, so t = ½
⇒ cosθ = ½
∴ The value of θ is 60°