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## haleyking345 Group Title Solving trig Equations a.) sin^2x=3 cos^2x one year ago one year ago

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1. haleyking345 Group Title

Please Help!!!

2. jtvatsim Group Title

reposting question in better format: $\sin^2(x) = 3\cos^2(x)$

3. haleyking345 Group Title

I do not have a clue where to even start.

4. jtvatsim Group Title

well, as it stands it looks pretty bad... do you remember what sin(x)/cos(x) is equal to?

5. haleyking345 Group Title

tan x

6. jtvatsim Group Title

good! now, let's use that to make this question simpler. divide both sides by cos^2(x) and it starts looking better.

7. jtvatsim Group Title

You should get this:$\tan^2(x) = 3$

8. haleyking345 Group Title

So then you square root it right?

9. jtvatsim Group Title

yes!

10. jtvatsim Group Title

do not forget that you will have a positive and negative root

11. haleyking345 Group Title

ok thank you

12. jtvatsim Group Title

Let me know if you need any further help good luck!

13. SithsAndGiggles Group Title

Alternatively, you can use the identity $\sin^2x +\cos^2x=1$ Rewriting the left (or right side, appropriately), you have $\sin^2x=3(1-\sin^2x)\\ \sin^2x=3-3\sin^2x\\ 4\sin^2x=3\\ \sin^2x=\frac{3}{4}$

14. SithsAndGiggles Group Title

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.