Trigonometry Examples

$\sin^{2} (t) + \cos^{2} (t) + \tan^{2} (t)$

Step 1

Apply pythagorean identity.

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

Step 2

Rearrange terms.

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

Step 3

Apply pythagorean identity.

$\sec^{2} (t)$

Step 4

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

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

Step 5

Simplify the expression.

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Step 5.1

Apply the product rule to $\frac{1}{\cos (t)}$ .

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

Step 5.2

One to any power is one.

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

Step 5.3

Rewrite $1$ as $1^{2}$ .

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

Step 6

Rewrite $\frac{1^{2}}{\cos^{2} (t)}$ as ${(\frac{1}{\cos (t)})}^{2}$ .

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

Step 7

Convert from $\frac{1}{\cos (t)}$ to $\sec (t)$ .

$\sec^{2} (t)$