Question

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

Answer 1

Solve: sec x + csc x = 0

Explanation:

`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