First slide

Trigonometric equations

Question

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

Moderate

A

$π$
B

$\frac{π}{2}$
C

$3 π$
D

none of these

Solution

$x \in [0, 2 π] and y \in [0, 2 π]$ and sinx + siny = 2
This is possible only when sinx = 1 and siny = 1. Thus,
$x = π / 2 and y = π / 2$
Hence, x+y= $π$

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