Question

If $k$ be the perimeter of the $\triangle A B C$, then $b \cos ^ { 2 } \frac { C } { 2 } + c \cos ^ { 2 } \frac { B } { 2 }$ is equal to

• A. k
• B. 2k
• C. $\frac { k } { 2 }$
• D. None of these

Answer 1

Answer: (C)

$\frac { k } { 2 }$

Answer 2

$b \cos ^ { 2 } \frac { C } { 2 } + c \cos ^ { 2 } \frac { B } { 2 } = \frac { b } { 2 } ( 1 + \cos C ) + \frac { c } { 2 } ( 1 + \cos B )$

= $\frac { b } { 2 } + \frac { c } { 2 } + \frac { 1 } { 2 } ( b \cos C + c \cos B )$ = $\frac { a + b + c } { 2 } = \frac { k } { 2 }$.