1. ## Solving Trigonometric Equations

How do you solve:

$3\cot^2 {x} + 4\csc^2 {x} = -4$

and

$2\sin {x} \cos {x} +4\sin {x} = \cos {x} +2$

within $0 \leq x \leq 2\pi$ ?

2. Originally Posted by chrozer
How do you solve:

$3\cot^2 {x} + 4\csc^2 {x} = -4$

note: use the identity $\textcolor{red}{\csc^2{x} = 1 + \cot^2{x}}$

and

$2\sin {x} \cos {x} +4\sin {x} = \cos {x} +2$

factor ... $\textcolor{red}{2\sin{x}(\cos{x} + 2) = \cos{x} + 2}$

so ... $\textcolor{red}{2\sin{x}}$ must equal what?

within $0 \leq x \leq 2\pi$ ?
hope it helps.

3. Thnx I got it now.