Question

In a $\triangle A B C , \frac { \cos C + \cos A } { c + a } + \frac { \cos B } { b }$ is equal to

• A. $\frac { 1 } { a }$
• B. $\frac { 1 } { b }$
• C. $\frac { 1 } { c }$
• D. $\frac { c + a } { b }$

Answer 1

Answer: (B)

$\frac { 1 } { b }$

Answer 2

$\frac { \cos C + \cos A } { c + a } + \frac { \cos B } { b }$ = $\frac { ( b \cos C + b \cos A ) + ( c \cos B + a \cos B ) } { b ( c + a ) }$

=$\frac { ( b \cos C + c \cos B ) + ( b \cos A + a \cos B ) } { b ( c + a ) }$=$\frac { a + c } { b ( c + a ) }$

(Using projection formulae) = $\frac { 1 } { b }$.