Quantitative Aptitude Ques 2426
Question: The value of $ \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} $ is equal to
Options:
A) $ \cos ecx+\cot x $
B) $ \cos ecx+\tan x $
C) $ \sec x+\tan x $
D) $ \cos ecx-\cot x $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\times \frac{(\sqrt{1+\sin x}+\sqrt{1-\sin x})}{(\sqrt{1-\sin x}+\sqrt{1-\sin x})} $
$ \Rightarrow $ $ \frac{{{(\sqrt{1+\sin x}+\sqrt{1-\sin x})}^{2}}}{1+\sin x-(1-\sin x)} $
$ \Rightarrow $ $ \frac{1+\sin x+1-\sin x+2,(\sqrt{1+\sin x}.\sqrt{1-\sin x}}{2\sin x} $
$ \Rightarrow $ $ \frac{2+2,(\sqrt{1+\sin x}.\sqrt{1-\sin x}}{2\sin x} $
$ \Rightarrow $ $ \cos ecx+\frac{2,(\sqrt{1-{{\sin }^{2}}x}}{2\sin x} $
$ \Rightarrow $ $ \cos ec,x+\frac{\cos x}{\sin x}=\cos ec,x+\cot x $
BETA
