cos 57° + sin 27° =
1. cos 30°
2. cos 3°
3. sin 3°
4. None of these
1. cos 30°
2. cos 3°
3. sin 3°
4. None of these
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Correct Answer – Option 2 : cos 3°
Given
cos 57° + sin 27°
Formula Used
cos(90° – θ) = sinθ
sinC + sinD = 2 × sin(C + D)/2 × cos(C – D)/2
Calculation
cos(90° – θ) = sinθ
⇒ cos 57° + sin 27° = cos (90° – 33°) + sin 27°
⇒ sin 33° + sin 27°
⇒ 2sin (33° + 27°)/2 × cos(33° – 27°)/2
⇒ 2sin30° × cos 3°
⇒ 2 × 1/2 cos 3°
⇒ cos 3°
∴ The required answer is cos3°