Show that the equation
3cosϕ(tanϕsinϕ+1)=8cosϕ+1 3 \cos \phi ( \tan \phi \sin \phi + 1 ) = 8 \cos \phi + 1 3cosϕ(tanϕsinϕ+1)=8cosϕ+1can be written in the form
3cos2ϕ+5cosϕ−2=0 3 \cos^2 \phi + 5 \cos \phi - 2 = 0 3cos2ϕ+5cosϕ−2=0A mechanical sensor detects oscillations described by the phase equation
3cos3x(tan3xsin3x+1)=8cos3x+1 3 \cos 3x ( \tan 3x \sin 3x + 1 ) = 8 \cos 3x + 1 3cos3x(tan3xsin3x+1)=8cos3x+1where x x\,x represents the angular position in degrees. Hence solve this equation for 0∘<x<180∘0^\circ < x < 180^\circ0∘<x<180∘, giving your answers to one decimal place.
