The general solution of \(\cos (x)-\sin (x)=0\) is

The general solution of \(\cos (x)-\sin (x)=0\) is
  1. \(n \pi-\frac{\pi}{4}, n \in Z\)
  2. \(2 n \pi+\frac{\pi}{4}, n \in Z\)
  3. \(n \pi+\frac{\pi}{4}, n \in Z\)
  4. \(2 n \pi-\frac{\pi}{4}, n \in Z\)

Solution

\(\begin{aligned} & \cos x-\sin x =0 \\ \Rightarrow & \cos x =\sin x \Rightarrow \tan x=1 \\ \Rightarrow & x =n \pi+\frac{\pi}{4} ;(n \in \mathbf{Z}) \end{aligned}\)

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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