Simplify (1-cos(x)^2)(cot(x)^2+1)

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

Step 1

Apply pythagorean identity.

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

Step 2

Rearrange terms.

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

Step 3

Apply pythagorean identity.

$\sin^{2} (x) \csc^{2} (x)$

Step 4

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

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

Step 5

Simplify the expression.

Apply the product rule to $\frac{1}{\sin (x)}$ .

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

One to any power is one.

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

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

Step 6

Cancel the common factor of $\sin^{2} (x)$ .

Cancel the common factor.

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

Rewrite the expression.

$1$

$1$

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