An automated tracking sensor for a wind turbine calculates its optimal inclination angle θ\thetaθ relative to the wind direction. For a specific range of wind speeds, the mechanical equilibrium of the sensor is maintained when
Show that the equation 6tanθ=cosθ6 \tan \theta = \cos \theta6tanθ=cosθ may be rewritten in the form sin2θ+6sinθ−1=0\sin^2 \theta + 6 \sin \theta - 1 = 0sin2θ+6sinθ−1=0
Hence solve, for 0∘≤x≤180∘0^\circ \le x \le 180^\circ0∘≤x≤180∘, the equation 6tan(2x+10∘)=cos(2x+10∘)6 \tan (2x + 10^\circ) = \cos (2x + 10^\circ)6tan(2x+10∘)=cos(2x+10∘) giving your answers to 2 decimal places.