How do you solve $secx+cscx=0$ ?

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Answer 1 · 2015-07-10T17:54:43

Solve: sec x + csc x = 0

$f(x) = 1/cos x + 1/sin x = (sin x + cos x)/(sin.x.cos x) = 0$ ->

$sin x + cos x = sqrt2.sin (x + pi/4) = 0$

$sin (x + pi/4) = 0 -> (x + pi/4) = 0 and (x + pi/4) = pi$

$x + pi/4 = 0 -> x = - pi/4$

$x + pi/4 = pi -> x = pi - pi/4 = 3pi/4$
Check
$x = -pi/4 -> sec (-pi/4) + csc (-pi/4) = 2/(sqrt2) - 2/(sqrt2) = 0$ . OK

$x = (3pi)/4 -> sec ((3pi)/4) + csc ((3pi)/4) = -2/(sqrt2) + 2/(sqrt2) = 0$ . OK

How do you solve secx+cscx=0secx+cscx=0?