If $s i n x + s i n y + s i n z = 3$ . Find the value of $c o s x + c o s y + c o s z$ .

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Solution

Given, $s i n x + s i n y + s i n z = 3$

As value of sin function lies in the interval [-1,1], so, $s i n x + s i n y + s i n z = 3$ is possible only when,

$s i n x = s i n y = s i n z = 1$

$⟹ s i n x + s i n y + s i n z = s i n 90$

$⟹ x = y = z = 90$

Therefore,
$c o s x + c o s y + c o s z = c o s 90 + c o s 90 + c o s 90 = 0$

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