How to solve 3sin^2x= cos^2x

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I'll try it. I just went through this twice on scratch paper.  The first time was to see if I could do it, and the second time was because the first result I got was ridiculous.  But I think I got it. You said                                                 3sin²(x) = cos²(x) Use this trig identity:  sin²(x) = 1 - cos²(x)                                       Plug it into the original equation for (x).                                                      3(1 - cos²(x) )  =  cos²(x) Remove parentheses on the left:    3 - 3cos²(x)  =  cos²(x) Add  3cos²(x)  to each side:            3                  =  4cos²(x) Divide each side by  4 :                  3/4  =  cos²(x) Take the square root of each side:    cos(x) = (√3) / 2 . There it is ... the cosine of the unknown angle. Now you just go look it up in a book with a table cosines, or else pinch it through your computer or your calculator, or else just remember that you've learned that                            cos( 30° )  =  (√3) / 2 .

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