Question

In triangla ABC show that 2(bc cos A + ca cos B + ab cos C) = a^2 + b^2 + c^2​

Answer 1

Answer:

2(bc cos A + ca cos B + ab cos C) = a² + b² + c²

Step-by-step explanation:

Here, we will use the projection formula

We know that, In any triangle ABC

• a = b cosC + c cosB
• b = c cosA + a cosC
• c = a cosB + b cosA

Now, from the question,

2( bc cos A + ca cos B + ab cos C )

= 2bc cos A + 2ca cos B + 2ab cos C

= bc cos A + ca cos B + ab cos C + bc cos A + ca cos B + ab cos C

= a( b cosC + c cosB ) + b( c cosA + a cosC ) + c( a cosB + b cosA )

=a(a) + b(b) + c(c)

= a² + b² + c².

Hence, Proved