How do you solve $cos x = sin x$ $cosx=sinx$ and find all exact general solutions?

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How do you solve $cos x = sin x$ $cosx=sinx$ and find all exact general solutions?

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Answer 1 · 2016-07-22T02:45:21

$x = \frac{π}{4} + 2 k π$ $x = pi/4 + 2kpi$

Explanation:

cos x = sin x
Property of complementary arcs -->
$cos x = sin (\frac{π}{2} - x)$ $cos x = sin (pi/2 - x)$
There for:
sin x = sin (pi/2 - x)
There are 2 solutions:
a. $x = \frac{π}{2} - x$ $x = pi/2 - x$ --> $2 x = \frac{π}{2}$ $2x = pi/2$ --> $x = \frac{π}{4}$ $x = pi/4$
b. $x = π - (\frac{π}{2} - x) = \frac{π}{2} + x$ $x = pi - (pi/2 - x) = pi/2 + x$
Undefined equation .
General answer:
$x = \frac{π}{4} + 2 k π$ $x = pi/4 + 2kpi$

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How do you solve $cos x = sin x$ $cosx=sinx$ and find all exact general solutions?

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How do you solve $cos x = sin x$ $cosx=sinx$ and find all exact general solutions?