Answer:
Step-by-step explanation:
[tex]\displaystyle\sin^2{\theta}+\cos^2{\theta}=1 \qquad\text{Pythagorean identiy}\\\\\sin{\theta}=\sqrt{1-\cos^2{\theta}} \qquad\text{solved for sine}\\\\\tan{\theta}=\frac{\sin{\theta}}{\cos{\theta}}=\frac{\sqrt{1-\cos^2{\theta}}}{\cos{\theta}}[/tex]
_____
If you draw a triangle with a hypotenuse of 1 and an "adjacent" leg of "cos", then using the Pythagorean theorem, you can see that the "opposite" leg will be √(1-cos²) and the tangent will be (√(1-cos²))/cos. Whether or not you're allowed to draw such a triangle on paper, you can certainly do it in your mind.
