Question

A + b + c = 2 pi then cos a = 2 cos b into cos c then find the value of tan a

Answer 1

$a + b + c = 2\pi \\ a = 2\pi - (b + c )\\ \tan(a) = \tan(2\pi - (b + c)) \\ \tan(a) = \tan(b + c ) \\ \tan(a) = \frac{ \tan(b) + \tan(c) }{1 - \tan(b) \tan(c) } \\ \tan(a) = \frac{ \sin(b) + \sin(c) }{\cos(b) \cos(c)\ - \sin(b) \sin(c) } \\ \tan(a) \: = \frac{2( \sin(b) + \sin(c)) }{} \\ \\ \cos (a)= 2 \cos (b)\cos (c) \\ \cos(a) = \cos(b + c) + \cos(b - c)$