Question

For what value of $\theta$, the equation $\sin \theta +\cos \theta$ is maximum.

Answer 1

Let $z=\sin \theta +\cos \theta$
$=\sqrt{2}\left[\sin (\frac{\pi }{4}+\theta )\right]$
z is maximum when $\sin (\frac{\pi }{4}+\theta )$ is 1
$\therefore \sin (\frac{\pi }{4}+\theta )=\sin \frac{\pi }{2}or\theta =\frac{\pi }{4}or{45}^0$