Critical $sin,cos$

Geometry Level 3

$\sin x+\sin y=1\\ \cos x+\cos y=0$

If $x,y\in \mathbb R^{+}$

What's the minimum value of $\large x+y=??$

None of these 0

\frac{\pi}{4}

\frac{\pi}{2}

\pi

1 solution

Md Mehedi Hasan
Nov 19, 2017

$sinx+siny=1\\2sin\frac{x+y}{2}cos\frac{x-y}{2}=1.............(i)$

Again $cosx+cosy=0\\2cos\frac{x+y}{2}cos\frac{x-y}{2}=0.............(ii)$

From $(ii)$ , $cos\frac{x-y}{2}\neq0$ because, if this right then it doesn't satisfy $(i)$ equation.

Then,

$cos\frac{x+y}{2}=0=cos\frac{\pi}{2}\\\frac{x+y}{2}=\frac{\pi}{2}\\\therefore x+y=\boxed{\pi}$

Bro...your solution has a bit of error...if sinx = siny =1, then sinx + siny =2, but have only given sinx + siny=1...

I guess you should make it sinx + siny... you have accidentally written = in place of +

Skanda Prasad - 3 years, 6 months ago

Thanks a lot. I made a mistake in typing. Now I have edited this....

Md Mehedi Hasan - 3 years, 6 months ago

Then what is $x, y$ ?

. . - 3 months, 1 week ago