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jtvatsimBest ResponseYou've already chosen the best response.1
reposting question in better format: \[\sin^2(x) = 3\cos^2(x)\]
 one year ago

haleyking345Best ResponseYou've already chosen the best response.0
I do not have a clue where to even start.
 one year ago

jtvatsimBest ResponseYou've already chosen the best response.1
well, as it stands it looks pretty bad... do you remember what sin(x)/cos(x) is equal to?
 one year ago

jtvatsimBest ResponseYou've already chosen the best response.1
good! now, let's use that to make this question simpler. divide both sides by cos^2(x) and it starts looking better.
 one year ago

jtvatsimBest ResponseYou've already chosen the best response.1
You should get this:\[\tan^2(x) = 3\]
 one year ago

haleyking345Best ResponseYou've already chosen the best response.0
So then you square root it right?
 one year ago

jtvatsimBest ResponseYou've already chosen the best response.1
do not forget that you will have a positive and negative root
 one year ago

jtvatsimBest ResponseYou've already chosen the best response.1
Let me know if you need any further help good luck!
 one year ago

SithsAndGigglesBest ResponseYou've already chosen the best response.0
Alternatively, you can use the identity \[\sin^2x +\cos^2x=1\] Rewriting the left (or right side, appropriately), you have \[\sin^2x=3(1\sin^2x)\\ \sin^2x=33\sin^2x\\ 4\sin^2x=3\\ \sin^2x=\frac{3}{4}\]
 one year ago

SithsAndGigglesBest ResponseYou've already chosen the best response.0
Which gives you the difference of squares \[\sin^2x\left(\frac{\sqrt3}{2}\right)^2=0\\ \left(\sin x+\frac{\sqrt3}{2}\right)\left(\sin x\frac{\sqrt3}{2}\right)=0\] Easily solvable.
 one year ago
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