Question
Download Solution PDFUsing cos(A + B) = cos A cos B - sin A sin B, find the value of cos75°.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
cos(A + B) = cos A cos B - sin A sin B.
Calculation:
Cos 75° = cos (45° + 30°)
⇒ cos 45° × cos 30° - sin 45° × sin 30°
⇒ (1/√2) × (√3/2) - (1/√2) × (1/2)
⇒ (√3/2√2) - (1/2√2)
⇒ (√3 - 1)/2√2
⇒ √2 × (√3 - 1)/(2√2 × √2)
⇒ \(\frac{\sqrt6-\sqrt2}{4}\)
∴ The correct answer is \(\frac{\sqrt6-\sqrt2}{4}\).
Last updated on Jun 13, 2025
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