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

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

Step 1

Apply pythagorean identity.

$\cos^{2} (θ) (1 + \tan^{2} (θ))$

Step 2

Rearrange terms.

$\cos^{2} (θ) (\tan^{2} (θ) + 1)$

Step 3

Apply pythagorean identity.

$\cos^{2} (θ) \sec^{2} (θ)$

Step 4

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

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

Step 5

Simplify the expression.

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

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

One to any power is one.

$\cos^{2} (θ) \frac{1}{\cos^{2} (θ)}$

$\cos^{2} (θ) \frac{1}{\cos^{2} (θ)}$

Step 6

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

Cancel the common factor.

$\cos^{2} (θ) \frac{1}{\cos^{2} (θ)}$

Rewrite the expression.

$1$

$1$

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