First slide

Trigonometric equations

Question

If $x, y \in [0, 2 π]$ and $\sin x + \sin y = 2$ then the value of $x + y$ is

Very Easy

A

$π$
B

$\frac{π}{2}$
C

$3 π$
D

$\frac{3 π}{2}$

Solution

$x \in [0, 2 π], y \in [0, 2 π]$ and $\sin x + \sin y = 2$
$\Rightarrow \sin x = 1, \sin y = 1$
$\Rightarrow x = \frac{π}{2}, y = \frac{π}{2}$
$\Rightarrow x + y = \frac{π}{2} + \frac{π}{2} = π$

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