Question

How do you solve `csc^2 x - (cos^4 x + 2 cos^2 x sin^2 x + sin^4 x) = 0`?

Answer 1

`pi/2 + kpi`

Explanation:

First, simplify the expression in parentheses
#cos^4 x + 2 cos^2 x.sin^2 x + sin^4 x = #(cos^2 x + sin^2 x)^2 = 1^2 = 1#

The equation becomes:
`1/sin^2 x - 1 = 0`
`sin^2 x = 1`
`sin x = +- 1`

a. sin x = 1 --> `x = pi/2 + kpi`
b. sin x = -1 --> `x = (3pi)/2 + kpi`