How do you solve $cos(x/2) - sin(x) = 0$ ?

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How do you solve $cos(x/2) - sin(x) = 0$ ?

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Answer 1 · 2016-04-30T17:05:49

$pi + 2kpi$
$2kpi$
(5pi)/3 + 2kpi

Explanation:

Use trig identity: $sin x = 2sin (x/2).cos (x/2)$ . We get:
$cos (x/2)- sin (x/2).cos (x/2) = 0$
$cos (x/2)(1 - 2sin x) = 0$
a. $cos (x/2) = 0$ -->arc $x/2 = pi/2$ and arc $x = (3pi)/2$ -->
$x = pi$ and $x = 3pi.$
General answer --> $x = pi + 2kpi$
b. $sin (x/2) = 1/2$ .
Trig table and unit circle give:
$x/2 = pi/6$ and $x/2 = (5pi)/6$ -->
$x = (2pi)/6$ and $x = (5pi)/3$
General answers:
$x = pi + 2kpi$
$x = 2kpi$
$x = (5pi)/3 + 2kpi$

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How do you solve $cos(x/2) - sin(x) = 0$ ?

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