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

haleyking345
 one year ago
Best ResponseYou've already chosen the best response.0I do not have a clue where to even start.

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

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

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

haleyking345
 one year ago
Best ResponseYou've already chosen the best response.0So then you square root it right?

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

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

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

SithsAndGiggles
 one year ago
Best ResponseYou've already chosen the best response.0Which 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.
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