Precalculus Examples

$\sin (B) \sec (B) \cot (B) = 1$

Step 1

Start on the left side.

$\sin (B) \sec (B) \cot (B)$

Step 2

Convert to sines and cosines.

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Step 2.1

Apply the reciprocal identity to $\sec (B)$ .

$\sin (B) \frac{1}{\cos (B)} \cot (B)$

Step 2.2

Write $\cot (B)$ in sines and cosines using the quotient identity.

$\sin (B) \frac{1}{\cos (B)} \frac{\cos (B)}{\sin (B)}$

Step 3

Simplify.

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Step 3.1

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

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Step 3.1.1

Factor $\sin (B)$ out of $\sin (B) \frac{1}{\cos (B)}$ .

$\sin (B) (\frac{1}{\cos (B)}) \frac{\cos (B)}{\sin (B)}$

Step 3.1.2

Cancel the common factor.

$\sin (B) \frac{1}{\cos (B)} \frac{\cos (B)}{\sin (B)}$

Step 3.1.3

Rewrite the expression.

$\frac{1}{\cos (B)} \cos (B)$

Step 3.2

Combine $\frac{1}{\cos (B)}$ and $\cos (B)$ .

$\frac{\cos (B)}{\cos (B)}$

Step 3.3

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

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Step 3.3.1

Cancel the common factor.

$\frac{\cos (B)}{\cos (B)}$

Step 3.3.2

Rewrite the expression.

$1$

Step 4

Because the two sides have been shown to be equivalent, the equation is an identity.

$\sin (B) \sec (B) \cot (B) = 1$ is an identity