The general solution of the trigonometric equation sin⁡x+cos⁡x=1 is given by

A
$x = 2 n π$
B
$x = 2 n π + \frac{π}{2}$
C
$x = n π + (- 1)^{n} \frac{π}{4} - \frac{π}{4}$
D
none of these

Solution:

We have,

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

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

Solution:

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