Question

2/1+sin(x) = sin^2(x)+5/cos^2(x)​

Answer 1

`(2)/(1 + \sin(x) ) = \frac{ { \sin }^(2)x + 5 }{ { \cos}^(2)x }`

`(2)/(1 + \sin(x) ) ( (1 - \sin(x) )/(1 - \sin(x) ) ) = \frac{ { \sin }^(2) x + 5}{1 - { \sin}^(2) x}`

`2 - 2 \sin(x) = { \sin }^(2) x + 5`

`{ \sin }^(2) x + 2 \sin(x) + 3 = 0`

`{ \sin}^(2) x + 2 \sin(x) + 1 = - 2`

`{( \sin(x) + 1)}^(2) = - 2`

This equation has no solutions.