Evaluate (1+sin(3))/(2+tan(4))

$\frac{1 + \sin (3)}{2 + \tan (4)}$

Step 1

Rewrite $\tan (4)$ in terms of sines and cosines.

$\frac{1 + \sin (3)}{2 + \frac{\sin (4)}{\cos (4)}}$

Step 2

Multiply the numerator and denominator of the complex fraction by $\cos (4)$ .

Multiply $\frac{1 + \sin (3)}{2 + \frac{\sin (4)}{\cos (4)}}$ by $\frac{\cos (4)}{\cos (4)}$ .

$\frac{\cos (4)}{\cos (4)} \cdot \frac{1 + \sin (3)}{2 + \frac{\sin (4)}{\cos (4)}}$

Combine.

$\frac{\cos (4) (1 + \sin (3))}{\cos (4) (2 + \frac{\sin (4)}{\cos (4)})}$

Step 3

Apply the distributive property.

$\frac{\cos (4) \cdot 1 + \cos (4) \sin (3)}{\cos (4) \cdot 2 + \cos (4) \frac{\sin (4)}{\cos (4)}}$

Step 4

Reduce the expression by cancelling the common factors.

Cancel the common factor of $\cos (4)$ .

Cancel the common factor.

$\frac{\cos (4) \cdot 1 + \cos (4) \sin (3)}{\cos (4) \cdot 2 + \cos (4) \frac{\sin (4)}{\cos (4)}}$

Rewrite the expression.

$\frac{\cos (4) \cdot 1 + \cos (4) \sin (3)}{\cos (4) \cdot 2 + \sin (4)}$

Multiply $\cos (4)$ by $1$ .

$\frac{\cos (4) + \cos (4) \sin (3)}{\cos (4) \cdot 2 + \sin (4)}$

Step 5

Move $2$ to the left of $\cos (4)$ .

$\frac{\cos (4) + \cos (4) \sin (3)}{2 \cos (4) + \sin (4)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\cos (4) + \cos (4) \sin (3)}{2 \cos (4) + \sin (4)}$

Decimal Form:

$0.50839283 \dots$