A deep-space communication laser's alignment angle ψ \psi\,ψ is modeled by the equation
6sinψcosψcosψ+sinψ=(5+sec2ψ)(cosψ−sinψ) \frac{6 \sin \psi \cos \psi}{\cos \psi + \sin \psi} = (5 + \sec 2\psi)(\cos \psi - \sin \psi) cosψ+sinψ6sinψcosψ=(5+sec2ψ)(cosψ−sinψ)Show that this equation can be simplified to the form
6sin2ψ−10cos2ψ=2 6 \sin 2\psi - 10 \cos 2\psi = 2 6sin2ψ−10cos2ψ=2For an observation window 0<t<π0 < t < \pi0<t<π, determine the values of the signal time t t\,t satisfying
6sintcostcost+sint=(5+sec2t)(cost−sint) \frac{6 \sin t \cos t}{\cos t + \sin t} = (5 + \sec 2t)(\cos t - \sin t) cost+sint6sintcost=(5+sec2t)(cost−sint)giving your answers to 3 significant figures.
