Question

cos15°+sin15°/cos15°-sin15°=√3

Answer 1

Sol:
sin (A - B) = Sin A Cos B - Cos A sin B
Let A = 45° and B = 30°
sin (45° - 30°) = Sin 45° Cos 30° - Cos 45° sin 30°
sin (45° - 30°) = (1/√2)(√3/2) - (1/√2)(1/2)
sin 15° = (√3 - 1) / (2√2)

cos (A - B) = Cos A Cos B + Sin A sin B
Let A = 45° and B = 30°
cos (45° - 30°) = Cos 45° Cos 30° + Sin 45° sin 30°
cos (45° - 30°) = (1/√2)(√3/2) + (1/√2)(1/2)
cos 15° = (√3 + 1) / (2√2)

Answer 2

sin(15) + cos(15) / (sin(15) - cos(15)
sin(15) + cos(15) * (sin(15) + cos(15) / (sin(15) - cos(15) * sin(15) + cos(15)
(sin(15)^2 + 2sin(15)cos(15) + cos(15)^2) / (sin(15)^2 - cos(15)^2
sin(15)^2 + cos(15)^2 + 2sin(15) cos (15) / cos(15)^2 - sin(15)^2
1 + sin(2 * 15) / cos(2 * 15)
1 + sin(30)) / cos(30) 
1 + 1/2) / (3)/2)
(3/2) / √(3)/2) 

√ 3/(3)
√(3)