The acute angle between the lines $x-y=0$, and $y=0$ is

The acute angle between the lines $x-y=0$, and $y=0$ is
  1. $\frac{\pi}{6}$
  2. $\frac{\pi}{4}$
  3. $\frac{\pi}{3}$
  4. $\frac{5 \pi}{6}$

Solution

Equation of given lines $x-y=0$ and $y=0$. $ \begin{aligned} \theta & =\cos ^{-1}\left(\frac{|1 \times 0-1 \times 1+0 \times 0|}{\sqrt{1+1} \sqrt{1}}\right) \\ & =\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\pi}{4} \end{aligned} $

Asked in: AP EAMCET 2020 (22 Sep Shift 1)

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