Simplify cos(x)^2+tan(x)sin(x)cos(x)

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

Step 1

Simplify each term.

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

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

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

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Cancel the common factor of $\cos (x)$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Rearrange terms.

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

Step 3

Apply pythagorean identity.

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