Question

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

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