Answer
$cos~\theta=\sqrt {1-sin^2\theta}$
$tan~\theta=\frac{sin~\theta}{\sqrt {1-sin^2\theta}}$
$cot~\theta=\frac{\sqrt {1-sin^2\theta}}{sin~\theta}$
$csc~\theta=\frac{1}{sin~\theta}$
$sec~\theta=\frac{1}{\sqrt {1-sin^2\theta}}$
Work Step by Step
$sin^2\theta+cos^2\theta=1$
$cos^2\theta=1-sin^2\theta$
$cos~\theta=\sqrt {1-sin^2\theta}$
$tan~\theta=\frac{sin~\theta}{cos~\theta}=\frac{sin~\theta}{\sqrt {1-sin^2\theta}}$
$cot~\theta=\frac{1}{tan\theta}=\frac{\sqrt {1-sin^2\theta}}{sin~\theta}$
$csc~\theta=\frac{1}{sin~\theta}$
$sec~\theta=\frac{1}{cos~\theta}=\frac{1}{\sqrt {1-sin^2\theta}}$
