TITLE: Trigonometry equation $\sin(x)+\cos(x)-\tan(x)=0.4$
QUESTION [5 upvotes]: There's some way to find $x$ here ?
$$\sin(x)+\cos(x)-\tan(x)=0.4$$

REPLY [4 votes]: Avoid squaring wherever practicable as it immediately introduces extraneous roots 
Using  Weierstrass substitution we have
$$\frac{2t}{1+t^2}+\frac{1-t^2}{1+t^2}-\frac{2t}{1-t^2}=0.4$$ where $t=\tan\frac x2$
On rearrangement we have a Biquadratic Equation in $t$ with no extraneous root, find the answer here