Show that the equation
3cosϕ(tanϕsinϕ+1)=8cosϕ+13 \cos \phi ( \tan \phi \sin \phi + 1 ) = 8 \cos \phi + 13cosϕ(tanϕsinϕ+1)=8cosϕ+1
can be written in the form
3cos2ϕ+5cosϕ−2=03 \cos^2 \phi + 5 \cos \phi - 2 = 03cos2ϕ+5cosϕ−2=0
A mechanical sensor detects oscillations described by the phase equation
3cos3x(tan3xsin3x+1)=8cos3x+13 \cos 3x ( \tan 3x \sin 3x + 1 ) = 8 \cos 3x + 13cos3x(tan3xsin3x+1)=8cos3x+1
where 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.