Trigonometric Identities Question 329
Question: If $ \sin A+\cos A=\sqrt{2}, $ then $ {{\cos }^{2}}A= $
Options:
A) $ \frac{1}{4} $
B) $ \frac{1}{2} $
C) $ \frac{1}{\sqrt{2}} $
D) $ \frac{3}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \sin A+\cos A=\sqrt{2} $ . On squaring both the sides
Þ $ 1+\sin 2A=2,\Rightarrow \sin 2A=1=\sin 90^{o} $
Þ $ 2A=90^{o} $ or $ A=45^{o} $ Now, $ {{\cos }^{2}}A={{(\cos 45^{o})}^{2}}={{( \frac{1}{\sqrt{2}} )}^{2}}=\frac{1}{2} $ .
BETA
