Trigonometric Equations Question 95
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} $ .
BETA
