(tanθ + cotθ) (cosθ + sinθ)= sec θ + cosθ
(tanθ+cotθ)(cosθ+sinθ)=secθ + cosθ
You asked:
Solve the system of equations:\[\begin{aligned}\left(\tan\left( θ \right) + \cot\left( θ \right)\right) \cdot \left(\cos\left( θ \right) + \sin\left( θ \right)\right) &= \sec\left( θ \right) + \cos\left( θ \right)\\\left(\tan\left( θ \right) + \cot\left( θ \right)\right) \cdot \left(\cos\left( θ \right) + \sin\left( θ \right)\right) &= \sec\left( θ \right) + \cos\left( θ \right)\end{aligned}\]