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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