How do you solve $cosx=sinx$ ?

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How do you solve $cosx=sinx$ ?

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Answer 1 · 2016-08-09T15:57:23

$pi/4 or 45^@$

Explanation:

Property of complementary arcs -->
$cos x = sin (pi/2 - x)$
There for,
$sin x = sin (pi/2 - x)$
a. $x = (pi/2 - x)$ --> $2x = pi/2$ --> $x = pi/4$
b. $x = pi - (pi/2 - x) = pi/2 + x$ (Rejected as non-sense)

Answer: $x = pi/4 or 45^@$
Check.
$x = pi/4$ --> $sin x = sqrt2/2$ --> $cos x = sqrt2/2$ . OK

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