Trigonometry Examples

$\frac{\tan^{2} (t) + 1}{1 + \cot^{2} (t)}$

Step 1

Apply pythagorean identity.

$\frac{\sec^{2} (t)}{1 + \cot^{2} (t)}$

Step 2

Apply pythagorean identity.

$\frac{\sec^{2} (t)}{\csc^{2} (t)}$

Step 3

Rewrite $\frac{\sec^{2} (t)}{\csc^{2} (t)}$ as ${(\frac{\sec (t)}{\csc (t)})}^{2}$ .

${(\frac{\sec (t)}{\csc (t)})}^{2}$

Step 4

Rewrite $\csc (t)$ in terms of sines and cosines.

${(\frac{\sec (t)}{\frac{1}{\sin (t)}})}^{2}$

Step 5

Rewrite $\sec (t)$ in terms of sines and cosines.

${(\frac{\frac{1}{\cos (t)}}{\frac{1}{\sin (t)}})}^{2}$

Step 6

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (t)}$ .

${(\frac{\sin (t)}{\cos (t)})}^{2}$

Step 7

Convert from $\frac{\sin (t)}{\cos (t)}$ to $\tan (t)$ .

$\tan^{2} (t)$