Solve for X? 3sin2 x= Cos2 x ?

Question

Solve for X? 3sin2 x= Cos2 x ?

Answer 1

It's been a while...

Use identiy:

sin^2(x) + cos^2(x) = 1

SO...

3sin^2 x = cos^2 x

3sin^2 x = 1 - sin^2 x (from identity)

3sin^2 x + sin^2 x = 1

4sin^2 x = 1

sin^2 x = 1/4

(sin x)(sin x) = 1/4

sqrt (sin x)(sin x) = sqrt 1/4

so...

sin x = 1/2

x = 30 degrees I think.

Answer 2

divide both sides by Cos^2 x to get 3 tan^2 x=1 or tan^2 x = 1/3.   Now tan=1/sqrt(3).  Recognize what type right triangle has these numbers as the proportion for the opposite and adjacent sides?