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Q.

$The general solution of the trigonometric equation \sin x - \cos x = 1 is given by$

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a

$x = 2 n π, n \in I$

b

$x = n π + {(- 1)}^{n} \frac{π}{4} + \frac{π}{4}, n \in I$

c

$x = 2 n π + \frac{π}{2}, n \in I$

d

$x = n \frac{π}{2}, n \in I$

answer is B.

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Detailed Solution

$\begin{array}{l} \sin x - \cos x = 1 \\ \frac{1}{\sqrt{2}} \sin x - \frac{1}{\sqrt{2}} \cos x = \frac{1}{\sqrt{2}} \\ \Rightarrow \sin (x - \frac{π}{4}) = \sin \frac{π}{4} \\ \Rightarrow x - \frac{π}{4} = n π + {(- 1)}^{n} \frac{π}{4} \Rightarrow x = n π + {(- 1)}^{n} \frac{π}{4} + \frac{π}{4} \end{array}$

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