Algebra Examples

$\tan (A) - \csc (A) \sec (A) (1 - \cos^{2} (A))$

Step 1

Factor $1$ out of $\tan (A) - \csc (A) \sec (A) (1 - \cos^{2} (A))$ .

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Step 1.1

Multiply by $1$ .

$1 \tan (A) - \csc (A) \sec (A) (1 - \cos^{2} (A))$

Step 1.2

Factor $1$ out of $- \csc (A) \sec (A) (1 - \cos^{2} (A))$ .

$1 \tan (A) + 1 (- \csc (A) \sec (A) (1 - \cos^{2} (A)))$

Step 1.3

Factor $1$ out of $1 \tan (A) + 1 (- \csc (A) \sec (A) (1 - \cos^{2} (A)))$ .

$1 (\tan (A) - \csc (A) \sec (A) (1 - \cos^{2} (A)))$

Step 2

Apply pythagorean identity.

$1 (\tan (A) - \csc (A) \sec (A) \sin^{2} (A))$

Step 3

Simplify terms.

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Step 3.1

Multiply $\tan (A) - \csc (A) \sec (A) \sin^{2} (A)$ by $1$ .

$\tan (A) - \csc (A) \sec (A) \sin^{2} (A)$

Step 3.2

Simplify each term.

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Step 3.2.1

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

$\frac{\sin (A)}{\cos (A)} - \csc (A) \sec (A) \sin^{2} (A)$

Step 3.2.2

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

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

Step 3.2.3

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

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

Step 3.2.4

Multiply $\frac{1}{\cos (A)}$ by $\frac{1}{\sin (A)}$ .

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

Step 3.2.5

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

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Step 3.2.5.1

Move the leading negative in $- \frac{1}{\cos (A) \sin (A)}$ into the numerator.

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

Step 3.2.5.2

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

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

Step 3.2.5.3

Factor $\sin (A)$ out of $\sin^{2} (A)$ .

$\frac{\sin (A)}{\cos (A)} + \frac{- 1}{\sin (A) \cos (A)} (\sin (A) \sin (A))$

Step 3.2.5.4

Cancel the common factor.

$\frac{\sin (A)}{\cos (A)} + \frac{- 1}{\sin (A) \cos (A)} (\sin (A) \sin (A))$

Step 3.2.5.5

Rewrite the expression.

$\frac{\sin (A)}{\cos (A)} + \frac{- 1}{\cos (A)} \sin (A)$

Step 3.2.6

Combine $\frac{- 1}{\cos (A)}$ and $\sin (A)$ .

$\frac{\sin (A)}{\cos (A)} + \frac{- \sin (A)}{\cos (A)}$

Step 3.2.7

Move the negative in front of the fraction.

$\frac{\sin (A)}{\cos (A)} - \frac{\sin (A)}{\cos (A)}$

Step 3.3

Subtract $\frac{\sin (A)}{\cos (A)}$ from $\frac{\sin (A)}{\cos (A)}$ .

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