Question

How do you find the general solutions for `cos2xcscx-2cos2x=0`?

Answer 1

Use algebra

Explanation:

`cos 2x csc x - 2 cos 2x = 0`
`cos 2x (csc x - 2) = 0`
Solution A: `cos 2x = 0 \Rightarrow 2x = pmpi/2 + kpi \Rightarrow x = pi/4 (2kpm1), k in ZZ`
Solution B: `1/cos x = 2 \Rightarrow cos x = 1/2 \Rightarrow x = pmpi/3 + 2kpi = pi/3 (6k+-1), k in ZZ`
`therefore x = pi/4 (2kpm1)` or `x = pi/3 (6k+-1), k in ZZ`