Algebra Examples

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

Step 1

Apply pythagorean identity.

$\cos^{2} (θ) \cdot \tan (θ) \cdot \csc (θ)$

Step 2

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

$\cos^{2} (θ) \cdot \frac{\sin (θ)}{\cos (θ)} \cdot \csc (θ)$

Step 3

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

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Step 3.1

Factor $\cos (θ)$ out of $\cos^{2} (θ)$ .

$\cos (θ) \cos (θ) \cdot \frac{\sin (θ)}{\cos (θ)} \cdot \csc (θ)$

Step 3.2

Cancel the common factor.

$\cos (θ) \cos (θ) \cdot \frac{\sin (θ)}{\cos (θ)} \cdot \csc (θ)$

Step 3.3

Rewrite the expression.

$\cos (θ) \cdot \sin (θ) \cdot \csc (θ)$

Step 4

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

$\cos (θ) \sin (θ) \cdot \frac{1}{\sin (θ)}$

Step 5

Cancel the common factor of $\sin (θ)$ .

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Step 5.1

Factor $\sin (θ)$ out of $\cos (θ) \sin (θ)$ .

$\sin (θ) \cos (θ) \cdot \frac{1}{\sin (θ)}$

Step 5.2

Cancel the common factor.

$\sin (θ) \cos (θ) \cdot \frac{1}{\sin (θ)}$

Step 5.3

Rewrite the expression.

$\cos (θ)$