Question

If $\sin 3\theta +2\sin \theta \cos \theta +\cos 3\theta =1$, then $\tan \theta =?$

Answer 1

$sin3\theta +2sin\theta cos\theta +cos3\theta =13sin\theta -4si{n}^3\theta +2sin\theta cos\theta +4co{s}^3\theta -3cos\theta =13(sin\theta -cos\theta )-4(si{n}^3\theta -co{s}^3\theta )=si{n}^2\theta +co{s}^2\theta -2sin\theta cos\theta 3(sin\theta -cos\theta )-4(sin\theta -cos\theta )(si{n}^2\theta +sin\theta cos\theta +co{s}^2\theta )=(sin\theta -cos\theta {)}^2(sin\theta -cos\theta \left)\right[3-4(si{n}^2\theta +sin\theta cos\theta +co{s}^2\theta )]-(sin\theta -cos\theta {)}^2=0(sin\theta -cos\theta )[3-4(1+sin\theta cos\theta )-(sin\theta -cos\theta \left)\right]=0\therefore sin\theta -cos\theta =0ortan\theta =1$