Question

Sin 5π/12 - sin π/12 /cos 5π/12 +cosπ/12 =1/√3

Answer 1

you can see your answer

Answer 2

Given,

$\frac{\sin\frac{5\pi}{12}+\sin\frac{\pi}{12}}{\cos\frac{5\pi}{12}+\cos\frac{\pi}{12}}\\\;\\=\frac{\sin45+\sin15}{\cos45+\cos15}\\\;\\=\frac{2\sin(\frac{45+15}{2}).\cos(\frac{45-15}{2})}{2\cos(\frac{45+15}{2}).\cos(\frac{45-15}{2})}\\\;\\=\frac{\sin30}{\cos30}\\\;\\=\tan30\\\;\\=\frac{1}{\sqrt{3}}\\\;\\\;\\\;\textbf{Note;-}\\\;\\\;\sin C+\sin D=2\sin(\frac{C+D}{2}).\cos(\frac{C-D}{2})\\\;\\\cos C+\cos D=2\cos(\frac{C+D}{2}).\cos(\frac{C-D}{2})}$