Trigonometry! #35

Geometry Level 4

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

Note that for all the options, $n=0,±1,±2,...$

This problem is part of the set Trigonometry .

x=n\pi + (-1)^{n} \frac {\pi}{4} - \frac {\pi}{4}

x=2n\pi

x=2n\pi + \frac {\pi}{2}

None of these

1 solution

Sandeep Rathod
Feb 6, 2015

$\dfrac{1}{\sqrt{2}}\sin x + \dfrac{1}{\sqrt{2}}\cos x = \dfrac{1}{\sqrt{2}}$

$\sin x \cos \dfrac{\pi}{4} + \cos x \sin \dfrac{\pi}{4} = \dfrac{1}{\sqrt{2}}$

$\sin ( x + \dfrac{\pi}{4}) = \sin \dfrac{\pi}{4}$

$x + \dfrac{\pi}{4} = n\pi + (-1)^n (\dfrac{\pi}{4})$

$x = n\pi + (-1)^n (\dfrac{\pi}{4}) - \dfrac{\pi}{4}$

How do you go from the third to the fourth step?Can you explain briefly...Thanks

Anik Mandal - 5 years, 4 months ago