SOLUTION: Solve using the fact that tanx = sinx/cosx and the Pythagorean identity on the domain [0, 2π] the trigonometric equation tan^2 x + cos^2 x = 1 i have managed to substiture

Algebra ->  Trigonometry-basics -> SOLUTION: Solve using the fact that tanx = sinx/cosx and the Pythagorean identity on the domain [0, 2π] the trigonometric equation tan^2 x + cos^2 x = 1 i have managed to substiture      Log On


   

Question 729302: Solve using the fact that tanx = sinx/cosx and the Pythagorean identity on the domain [0, 2π]
the trigonometric equation tan^2 x + cos^2 x = 1
i have managed to substiture tan with sinx/cosx to get sin^2 x/cos^2 x+cos^2 x=1 then rearranged it to sin^2 x+cos^4 x=cos^2 x but i have no idea what to do from here and the answers that have full working are just confusing
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
tan^2 x + cos^2 x = 1
(sin^2x/cos^2x)+cos^2x=1
LCD:cos^2x
sin^2x+cos^4x=cos^2x
1-cos^2x+cos^4x=cos^2x
cos^4x-2cos^2x+1=0
(cos^2x-1)(cos^2x-1)=0
(cosx+1)(cosx-1)(cosx+1)(cosx-1)=0
..
cosx=-1
x=π(multiplicity 2)
..
cosx=1
x=0 (multiplicity 2)