Question 218323




Remember that *[Tex \LARGE \tan(x)=\frac{\sin(x)}{\cos(x)}] 



Also, we have another identity: *[Tex \LARGE \sin^2(x)+\cos^2(x)=1] which means that *[Tex \LARGE \sin(x)=\sqrt{1-\cos^2(x)}]



*[Tex \LARGE \tan(x)=\frac{\sin(x)}{\cos(x)}] ... Start with the first identity.



*[Tex \LARGE \tan(x)=\frac{\sqrt{1-\cos^2(x)}}{\cos(x)}] ... Plug in *[Tex \LARGE \sin(x)=\sqrt{1-\cos^2(x)}]



*[Tex \LARGE \frac{\sqrt{3}}{2}=\frac{\sqrt{1-\cos^2(x)}}{\cos(x)}] ... Plug in *[Tex \LARGE \tan(x)=\frac{\sqrt{3}}{2}]



Now let {{{z=cos(x)}}}



*[Tex \LARGE \frac{\sqrt{3}}{2}=\frac{\sqrt{1-z^2}}{z}] ... Replace each cosine with 'z'



I'm going to let you take it from here. You just need to solve for 'z' and then use the equation {{{z=cos(x)}}} to find 'x'. Let me know if you still need help.