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