0. Functions

Simplify the expression.

$\tan^2\theta-\sec^2\theta+1$

Simplify the expression.

$\frac{\tan\left(-\theta\right)}{\sec\left(-\theta\right)}$

Simplify the expression.

$\left(\frac{\tan^2\theta}{\sin^2\theta}-1\right)\csc^2\left(\theta\right)\cos^2\left(-\theta\right)$

Identify the most helpful first step in verifying the identity.

$\left(\frac{\tan^2\theta}{\sin^2\theta}-1\right)=\sec^2\theta\sin^2\left(-\theta\right)$

Prove the following identities.

$\sec\theta=\frac{1}{\cos\theta}$

Prove the following identities.

$\tan\theta=\frac{\sin\theta}{\cos\theta}$

Prove the following identities.

$\frac{\sin\theta}{1+\cos\theta}=\frac{1-\cos\theta}{\sin\theta}$

Prove the following identities.

$\tan2\theta=\frac{2\tan\theta}{1-\tan^2\theta}$