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Suraj Halder
Asked: 2022-11-07T02:50:19+05:30 In:

Consider the following statements and state which one is correct:

I. Sin 75° = (√3 + 1)/2√2

II. Cos 75° = (√3 – 1)/2√2


1. Only 1
2. Only 2
3. Both 1 and 2
4. Neither 1 nor 2

Consider the following statements and state which one is correct:

I. Sin 75° = (√3 + 1)/2√2

II. Cos 75° = (√3 – 1)/2√2


1. Only 1
2. Only 2
3. Both 1 and 2
4. Neither 1 nor 2
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1 Answer

  1. Correct Answer – Option 3 : Both 1 and 2

    Formula Used:

    Sin(A ± B) = SinACosB ± SinBCosA

    Cos(A + B) = CosACosB – SinBsinA

    Cos(A – B) = CosACosB + SinBsinA

    Calculation:

    We have to calculate the value of Sin 75°

    ∴ Sin 75° = Sin (45 + 30)° = Sin45°Cos30° + Sin30°Cos45°

    ⇒ Sin 75° = 1/√2 × √3/2 + 1/2 × 1/√2 = (√3 + 1)/2√2

    So, statement 1 is correct

    Now the value of Cos 75°

    ∴ Cos 75° = cos(45 – 30)° = Cos45°Cos30° – Sin45°sin30°

    ⇒ Cos 75° = 1/√2 × √3/2 – 1/2 × 1/√2 = (√3 – 1)/2√2

    So, statement 2 is correct

    Hence, option (3) is correct

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