যদি \(\cos ^2 θ=\frac{3}{4}\) হয়, যেখানে θ একটি সূক্ষ্মকোণ, তাহলে sin (θ + 30°) এর মান হল:

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SSC CGL 2023 Tier-I Official Paper (Held On: 25 Jul 2023 Shift 3)
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  1. 1
  2. \(\frac{1}{\sqrt{2}}\)
  3. \(\frac{1}{2}\)
  4. \(\frac{\sqrt{3}}{2}\)

Answer (Detailed Solution Below)

Option 4 : \(\frac{\sqrt{3}}{2}\)
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Detailed Solution

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প্রদত্ত:

Cos2 θ = 3/4

অনুসৃত সূত্র:

Cos 30° = Sin 60° = √3/2

গণনা:

Cos2 θ = 3/4

⇒ cos θ = √(3/4) = √3/2

 cos θ  = cos 30° 

⇒ θ = 30° 

sin (θ + 30°) =  sin (30° + 30°)

⇒ sin 60° = √3/2

∴ সঠিক উত্তর হল √3/2

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