The number of solutions of the equation $| cos x - sin x | = 2 cos x, x ϵ [0, 2 π]$ is

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Solution

The correct option is B
2

Three cases can be considered:

(i) $cos x = sin x = 0$ which is impossible

(ii) $cos x > sin x, 0 \leq x < \frac{π}{4} and \frac{5 π}{4} < x \leq 2 π$

$\Rightarrow 2 cos x = cos x - sin x$

$\Rightarrow tan x = - 1 \Rightarrow x = \frac{7 π}{4}$

(iii) $cos x < sin x \Rightarrow \frac{π}{4} < x < \frac{5 π}{4}$

then $x = {tan}^{- 1} 3$

So, there are 2 solutions.

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