Trigonometric Equations Question 75
Question: If $ \sin (A+B) $ =1 and $ \cos (A-B)=\frac{\sqrt{3}}{2}, $ then the smallest positive values of A and B are
Options:
A) $ 60^{o},30^{o} $
B) $ 75^{o},15^{o} $
C) $ 45^{o},60^{o} $
D) $ 45^{o},45^{o} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \sin (A+B)=1 $ and $ \cos (A-B)=\frac{\sqrt{3}}{2} $
$ \Rightarrow $ $ A+B=\frac{\pi }{2} $ and $ A-B=\frac{\pi }{6} $
$ \Rightarrow $ $ A=\frac{\pi }{3},,B=\frac{\pi }{6} $ .
BETA
