olve factorable trigonometric equations in quadratic form

Question

If −π≤α<π, find all values of α that satisfy the equation 3tan^2α−3tanα=0. Separate your answers with commas. Detailed answer thank you!

Answer 1

3tan^2(A) - 3tan(A) = 0

divide by 3 and factor out tan(A)

tan(A)[tan(A)-1] = 0

set each factor =0

tan(A)=0 and tan(A) = 1

A= tan^-1(0) and tan^-1(1)

A= 0, pi or -pi and A = pi/4 or 5pi/4

Angle Alpha =0, pi/4, pi, 5pi/4 + 2npi where n= any integers

but you restricted the solutions to -pi<A<pi (that was the original restriction, with a strict inequality, but it seems to have changed, with -pi<A instead of -pi<A on the left side)

A=0, pi/4, -3pi/4 for a strict inequality, -pi<A<pi

A=0, pi/4, -3pi/4, -pi for the -pi<A<pi restriction