Show that the equation
[6sinθcosθcosθ+sinθ=(4+2sec2θ)(cosθ−sinθ) [\frac{6 \sin \theta \cos \theta}{\cos \theta + \sin \theta} = (4 + 2\sec 2\theta)(\cos \theta - \sin \theta) [cosθ+sinθ6sinθcosθ=(4+2sec2θ)(cosθ−sinθ)can be written in the form
3sin2θ−4cos2θ=2 3 \sin 2\theta - 4 \cos 2\theta = 2 3sin2θ−4cos2θ=2Hence solve for 0<x<π0 < x < \pi0<x<π
[6sinxcosxcosx+sinx=(4+2sec2x)(cosx−sinx) [\frac{6 \sin x \cos x}{\cos x + \sin x} = (4 + 2\sec 2x)(\cos x - \sin x) [cosx+sinx6sinxcosx=(4+2sec2x)(cosx−sinx)giving your answers to 3 significant figures.
