Trigonometric-Equations Question 402

Question: The general solution of $ \sin x-\cos x=\sqrt{2} $ , for any integer n is

[Karnataka CET 2005]

Options:

A) $ n\pi $

B) $ 2n\pi +\frac{3\pi }{4} $

C) $ 2n\pi $

D) $ (2n+1),\pi $

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Answer:

Correct Answer: B

Solution:

  • $ \sin x\frac{1}{\sqrt{2}}-\cos x\frac{1}{\sqrt{2}}=1\Rightarrow \cos ( x+\frac{\pi }{4} )=-1 $
    Þ $ x+\frac{\pi }{4}=2n\pi \pm \pi \Rightarrow 2n\pi +\frac{3\pi }{4}or2n\pi -\frac{5\pi }{4} $ .