Trigonometry Examples

$\cos (y) \sin (y) (\sec (y) + \csc (y))$

Step 1

Simplify each term.

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Step 1.1

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

$\cos (y) \sin (y) (\frac{1}{\cos (y)} + \csc (y))$

Step 1.2

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

$\cos (y) \sin (y) (\frac{1}{\cos (y)} + \frac{1}{\sin (y)})$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$\cos (y) \sin (y) \frac{1}{\cos (y)} + \cos (y) \sin (y) \frac{1}{\sin (y)}$

Step 2.2

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

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Step 2.2.1

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

$\cos (y) (\sin (y)) \frac{1}{\cos (y)} + \cos (y) \sin (y) \frac{1}{\sin (y)}$

Step 2.2.2

Cancel the common factor.

$\cos (y) \sin (y) \frac{1}{\cos (y)} + \cos (y) \sin (y) \frac{1}{\sin (y)}$

Step 2.2.3

Rewrite the expression.

$\sin (y) + \cos (y) \sin (y) \frac{1}{\sin (y)}$

Step 2.3

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

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Step 2.3.1

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

$\sin (y) + \sin (y) \cos (y) \frac{1}{\sin (y)}$

Step 2.3.2

Cancel the common factor.

$\sin (y) + \sin (y) \cos (y) \frac{1}{\sin (y)}$

Step 2.3.3

Rewrite the expression.

$\sin (y) + \cos (y)$