Simplify (1+tan(x)^2)(1-sin(x)^2)

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

Rearrange terms.

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

Apply pythagorean identity.

$\sec^{2} (x) (1 - \sin^{2} (x))$

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

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

Simplify the expression.

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

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

One to any power is one.

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

Apply pythagorean identity.

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

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

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Cancel the common factor.

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

Rewrite the expression.

$1$

Simplify (1+tan(x)^2)(1-sin(x)^2)

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