Chapter 7 - Review Exercises - Page 552: 35

$x=0$ $x=\pi$ $x=\frac{\pi}{2}$

$cos^2x+sin^2x=1$ $cos^2x=1-sin^2x$ $cos^2x+sin~x=1$ $1-sin^2x+sin~x=1$ $-sin^2x+sin~x=0$ $-sin~x(sin~x-1)=0$ $-sin~x=0$ $sin~x=0$ $x=0$ or $x=\pi$ $sin~x-1=0$ $sin~x=1$ $x=\frac{\pi}{2}$