Question

In a triangle ABC, b cosC + c cos B is always less than b + c.

• A. True
• B. False

Answer 1

The correct option is A True

We know that in a triangle sum of two sides are always more than the third side.
We also know with the help of projection formula b cosC + c cos B = a
So, b + c > a
Or b + c > b cosC + c cos B
Therefore the given statement is true.
We can also verify the given statement in this way -
$bcosC\le b;-1\le cos\left(\theta \right)\le 1$
Similarly c $cosB\le c$
Also, b cos C becomes b when C = 0
And c cos B becomes c when C = 0
Which can never be the case in a triangle, therefore
b cos C + c cos B < b + c