SATHEE: Quantitative Aptitude Ques 2426

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 $

Quantitative Aptitude Ques 2425

Quantitative Aptitude Ques 2427

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