Question

If tan^(2)x = 4 - 2tanx, then tanx =

Answer 1

tan(x) = -1 ±√5

Explanation:

This is a quadratic equation in tan(x). Let z = tan(x). Then the equation is ...

z² = 4 - 2z

z² +2z = 4 . . . . . . . add 2z

z² + 2z + 1 = 5 . . . . add 1 to complete the square

(z +1)² = 5 . . . . . . . . write as a square

z +1 = ±√5 . . . . . . . square root

z = -1 ±√5 = tan(x) . . . . . subtract 1; use definition of z