Question

In $\Delta A B C$ if $\theta$ is any angle, then $b \cos (C+\theta)+c \cos (B-\theta)=$

• A. $a \cot \theta$
• B. $a \cos \theta$
• C. $a \tan \theta$
• D. $a \sin \theta$

Answer 1

Answer: (B)

Consider, $b \cos (C+\theta)+c \cos (B-\theta)$
$= b(\cos C \cos \theta-\sin C \sin \theta)+c$
$(\cos B \cos \theta+\sin B \sin \theta)$
$=\cos \theta(b \cos C+c \cos B)-\sin \theta$
$(b \sin C-c \sin B)$
$= a \cos \theta-\sin \theta .0$
$[\because$ By projection formula and by sine rule
$\frac{b}{\sin B} =\frac{c}{\sin C}$
$\Rightarrow b \sin C-c \sin B=0]$
$=a \cos \theta-\sin \theta \cdot 0=a \cos \theta$