Theorem :
In any triangle ABC, with sides a = BC, b = CA and c = BA, then prove that a = b cos C + c cos B, b = c cos A + a cos C, c = a cos B + b cos A



Proof:
Let ABC be any triangle and let AD be drawn perpendicular to BC.
(AD = h = altitude of triangle)In figure (i), we have
BD = x, DC = y


x + y = cos B + b cox C …. (iv)
From (i) and (iv), we have
BD = x, DC = y
In D ADB,
In D ADC,

From fig (iii),

Similarly, other three results can be proved.
