Trigonometric Identities Question 213
Question: Three expressions are given below:
$ Q_1=\sin (A+B)+\sin (B+C)+\sin (C+A) $ $ Q_2=\cos (A-B)+\cos (B-C)+\cos (C-A) $ $ Q_3=\sin A(\cos B+\cos C)+\sin B(\cos C+\cos A)+ $ $ \sin C(\cos A+\cos B) $ Which one of the following is correct?
Options:
A) $ Q_1=Q_2 $
B) $ Q_2=Q_3 $
C) $ Q_1=Q_3 $
D) All the expressions are different
Show Answer
Answer:
Correct Answer: C
Solution:
We take $ Q_3 $ first, $ Q_3=\sin A(\cos B+\cos C)+\sin B(\cos C+\cos A) $ $ +\sin C(\cos A+\cos B) $ $ =\sin AcosB+sinAcosC+sinBcosC+sinBcosA $ $ +\sin C\cos A+\sin C\cos B $ $ =\sin (A+B)+\sin (B+C)+\sin (C+A)=Q_1 $
$ \Rightarrow Q_3=Q_1 $
BETA
