Question

Expand sin(A+B+C) and and and and tan(A+B+C)

Answer 1

Step-by-step explanation:

We know that,

$\boxed{\rm \sin (α + β) = \sin α \cos β + \cos α \sin β}$

$\boxed{\rm \cos (α + β) = \cos α \cos β - \sin α \sin β}$

$\rm \sin (A + B+C) = \sin [(A+B)+C]$

$\rm \sin [(A+B)+C]= \sin (A+B) \cos C + \cos (A+B) \sin C$

$\rm = (\sin A \cos B+ \cos A \sin B ) \cos C + \cos (A+B) \sin C$

$\rm = (\sin A \cos B+ \cos A \sin B ) \cos C + (\cos A \cos B- \sin A \sin B) \sin C$

$\rm = \sin A \cos B \cos C+ \cos A \sin B \cos C + \cos A \cos B \sin C- \sin A \sin B \sin C$

$\rm = \cos A \cos B \cos C ( \tan A + \tan B + \tan C -\tan A \tan B \tanC)$