Question

Find x belongs to [0,pi/2] such that cos^2 x -3 sin^2 x = 0.

Answer 1

like a first step you know that cos^2 x +sin^2 x =1
so than from this sin^2 x = 1 -cos^2 x
subtitute this in equation in place of sin^2 x and will get one equation with cos x like unknowed term so note cos x = t and will get an quadratic equation in t
so what you need solve it and after you will get the roots of quadratic make them equal cos x and so will get the right result(s)

hope this will help you

good luck

Answer 2

cos^2 x -3 sin^2 x = 0.
cos^2 x =3 sin^2 x
sin^2 x /cos^2 x=1/3
tan^2x =1/3
tanx=1/sqrt3
tanx= tan30
x=npi+pi/3
x=30

Source: http://www.mathskey.com/question2answer/ask