Chapter 27, Problem 90PE

Prove that, if $I$ is the intensity of light transmitted by two polarizing filters with axes at an angle $\theta$ and $I\text{'}$ is the intensity when the axes are at an angle $90.0°-\theta$, then $I+I\text{'}=I_0$, the original intensity. (Hint: Use the trigonometric identities $\cos \left(90.0°-\theta \right)=\sin \theta$ and ${\cos }^2\theta +{\sin }^2\theta =1$ .)