Trigonometry Examples

\frac{2 + cos (a) tan (a) csc (a)}{sec (a)}

$\frac{2 + \cos (a) \tan (a) \csc (a)}{\sec (a)}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite in terms of sines and cosines, then cancel the common factors.

Tap for more steps...

Step 1.1.1

Reorder

cos (a)

$\cos (a)$ and

tan (a)

$\tan (a)$ .

\frac{2 + tan (a) cos (a) csc (a)}{sec (a)}

$\frac{2 + \tan (a) \cos (a) \csc (a)}{\sec (a)}$

Step 1.1.2

Rewrite

cos (a) tan (a)

$\cos (a) \tan (a)$ in terms of sines and cosines.

\frac{2 + \frac{sin (a)}{cos (a)} cos (a) csc (a)}{sec (a)}

$\frac{2 + \frac{\sin (a)}{\cos (a)} \cos (a) \csc (a)}{\sec (a)}$

Step 1.1.3

Cancel the common factors.

\frac{2 + sin (a) csc (a)}{sec (a)}

$\frac{2 + \sin (a) \csc (a)}{\sec (a)}$

\frac{2 + sin (a) csc (a)}{sec (a)}

$\frac{2 + \sin (a) \csc (a)}{\sec (a)}$

Step 1.2

Rewrite in terms of sines and cosines, then cancel the common factors.

Tap for more steps...

Step 1.2.1

Reorder

sin (a)

$\sin (a)$ and

csc (a)

$\csc (a)$ .

\frac{2 + csc (a) sin (a)}{sec (a)}

$\frac{2 + \csc (a) \sin (a)}{\sec (a)}$

Step 1.2.2

Rewrite

sin (a) csc (a)

$\sin (a) \csc (a)$ in terms of sines and cosines.

\frac{2 + \frac{1}{sin (a)} sin (a)}{sec (a)}

$\frac{2 + \frac{1}{\sin (a)} \sin (a)}{\sec (a)}$

Step 1.2.3

Cancel the common factors.

\frac{2 + 1}{sec (a)}

$\frac{2 + 1}{\sec (a)}$

\frac{2 + 1}{sec (a)}

$\frac{2 + 1}{\sec (a)}$

Step 1.3

Add

2

$2$ and

1

$1$ .

\frac{3}{sec (a)}

$\frac{3}{\sec (a)}$

\frac{3}{sec (a)}

$\frac{3}{\sec (a)}$

Step 2

Rewrite

sec (a)

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

\frac{3}{\frac{1}{cos (a)}}

$\frac{3}{\frac{1}{\cos (a)}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

3 cos (a)

$3 \cos (a)$