Trigonometry Examples

$\cos (x) (1 + \tan (x^{2}))$

Step 1

Rewrite $\tan (x^{2})$ in terms of sines and cosines.

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

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$\cos (x) \cdot 1 + \cos (x) \frac{\sin (x^{2})}{\cos (x^{2})}$

Step 2.2

Multiply $\cos (x)$ by $1$ .

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

Step 2.3

Combine $\cos (x)$ and $\frac{\sin (x^{2})}{\cos (x^{2})}$ .

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

Step 3

Simplify each term.

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Step 3.1

Separate fractions.

$\cos (x) + \frac{\sin (x^{2})}{1} \cdot \frac{\cos (x)}{\cos (x^{2})}$

Step 3.2

Rewrite $\frac{\cos (x)}{\cos (x^{2})}$ as a product.

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

Step 3.3

Write $\cos (x)$ as a fraction with denominator $1$ .

$\cos (x) + \frac{\sin (x^{2})}{1} (\frac{\cos (x)}{1} \cdot \frac{1}{\cos (x^{2})})$

Step 3.4

Simplify.

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Step 3.4.1

Divide $\cos (x)$ by $1$ .

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

Step 3.4.2

Convert from $\frac{1}{\cos (x^{2})}$ to $\sec (x^{2})$ .

$\cos (x) + \frac{\sin (x^{2})}{1} (\cos (x) \sec (x^{2}))$

Step 3.5

Divide $\sin (x^{2})$ by $1$ .

$\cos (x) + \sin (x^{2}) \cos (x) \sec (x^{2})$