Trigonometry Examples

$\cos (t) + \tan (t) \sin (t)$

Step 1

Simplify each term.

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Step 1.1

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

$\cos (t) + \frac{\sin (t)}{\cos (t)} \sin (t)$

Step 1.2

Multiply $\frac{\sin (t)}{\cos (t)} \sin (t)$ .

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Step 1.2.1

Combine $\frac{\sin (t)}{\cos (t)}$ and $\sin (t)$ .

$\cos (t) + \frac{\sin (t) \sin (t)}{\cos (t)}$

Step 1.2.2

Raise $\sin (t)$ to the power of $1$ .

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

Step 1.2.3

Raise $\sin (t)$ to the power of $1$ .

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

Step 1.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2.5

Add $1$ and $1$ .

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

Step 2

Simplify each term.

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Step 2.1

Factor $\sin (t)$ out of $\sin^{2} (t)$ .

$\cos (t) + \frac{\sin (t) \sin (t)}{\cos (t)}$

Step 2.2

Separate fractions.

$\cos (t) + \frac{\sin (t)}{1} \cdot \frac{\sin (t)}{\cos (t)}$

Step 2.3

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

$\cos (t) + \frac{\sin (t)}{1} \tan (t)$

Step 2.4

Divide $\sin (t)$ by $1$ .

$\cos (t) + \sin (t) \tan (t)$