Find all exact solutions that exist on the interval [0, 2π). 1 − 2 tan(ω) = tan2(ω) w =

A possible solution: First add 1 to both sides and reduce the RHS via the Pytagorean identity.

Rewrite and in terms of and :

Multiply both sides by :

Use the double angle identities:

Divide both sides by :

Now, for , or , where is any integer. will fall in the interval for , which means we have

its b

step-by-step explanation:

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!