Question Detail

cos15° = cos(45°-30°) = cos45°cos30° + sin45°sin30° = (√2/2)(√3/2) + (√2/2)(1/2) = √2/2 × (√3/2 + 1/2) = √2(√3+1)/4. sin15° = sin(45°-30°) = sin45°cos30° - cos45°sin30° = (√2/2)(√3/2) - (√2/2)(1/2) = √2/2 × (√3/2 - 1/2) = √2(√3-1)/4. Then (cos15°+sin15°)/(cos15°-sin15°) = [√2(√3+1)/4 + √2(√3-1)/4] / [√2(√3+1)/4 - √2(√3-1)/4] = [√2(√3+1+√3-1)/4] / [√2(√3+1-√3+1)/4] = (2√3)/(2) = √3.