1.solve for x in $\displaystyle sinx tanx+ tanx-2sinx+cosx=0$ for 0<orequalx<or equal $\displaystyle 2\pi$ rads
2. find the exact value of $\displaystyle (\frac{7\pi}{6})$
I tried another way, but that doesn't lead to an exact solution.
$\displaystyle \sin x-2\sin x\cos x+1=0$
$\displaystyle 2\sin\frac{x}{2}\cos\frac{x}{2}\left(\sin^2\frac{x }{2}+\cos^2\frac{x}{2}\right)-$
$\displaystyle -4\sin\frac{x}{2}\cos\frac{x}{2}\left(\cos^2\frac{x }{2}-\sin^2\frac{x}{2}\right)+\left(\sin^2\frac{x}{2}+\ cos^2\frac{x}{2}\right)^2=0$
$\displaystyle \sin^4\frac{x}{2}+6\sin^3\frac{x}{2}\cos\frac{x}{2 }+2\sin^2\frac{x}{2}\cos^2\frac{x}{2}-2\sin\frac{x}{2}\cos^3\frac{x}{2}+\cos^4\frac{x}{2 }=0$
Divide by $\displaystyle \cos^4\frac{x}{2}$ and let $\displaystyle \tan\frac{x}{2}=t$
$\displaystyle t^4+6t^3+2t^2-2t+1=0$
$\displaystyle (t+1)(t^3+5t^2-3t+1)=0$
$\displaystyle t=-1$ which is not good because $\displaystyle x\neq\frac{(2k+1)\pi}{2}$
$\displaystyle t^3+5t^2-3t+1=0$ which has an irational solution.