Basic Math Examples

$4 \cos (45) \cdot (c t g (60)) - 3 \sin (45)$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

$4 \frac{\sqrt{2}}{2} \cdot (c t g (60)) - 3 \sin (45)$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $4$ .

$2 (2) \frac{\sqrt{2}}{2} \cdot (c t g (60)) - 3 \sin (45)$

Step 1.2.2

Cancel the common factor.

$2 \cdot 2 \frac{\sqrt{2}}{2} \cdot (c t g (60)) - 3 \sin (45)$

Step 1.2.3

Rewrite the expression.

$2 \sqrt{2} \cdot (c t g (60)) - 3 \sin (45)$

Step 1.3

Move $60$ to the left of $c t g$ .

$2 \sqrt{2} \cdot (60 \cdot (c t g)) - 3 \sin (45)$

Step 1.4

Multiply $60$ by $2$ .

$120 \sqrt{2} (c t g) - 3 \sin (45)$

Step 1.5

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$120 \sqrt{2} c t g - 3 \frac{\sqrt{2}}{2}$

Step 1.6

Combine $- 3$ and $\frac{\sqrt{2}}{2}$ .

$120 \sqrt{2} c t g + \frac{- 3 \sqrt{2}}{2}$

Step 1.7

Move the negative in front of the fraction.

$120 \sqrt{2} c t g - \frac{3 \sqrt{2}}{2}$

Step 2

Reorder the factors of $120 \sqrt{2} c t g$ .

$120 c g t \sqrt{2} - \frac{3 \sqrt{2}}{2}$

Step 3

To write $120 c g t \sqrt{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$120 c g t \sqrt{2} \cdot \frac{2}{2} - \frac{3 \sqrt{2}}{2}$

Step 4

Combine $120 c g t \sqrt{2}$ and $\frac{2}{2}$ .

$\frac{120 c g t \sqrt{2} \cdot 2}{2} - \frac{3 \sqrt{2}}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{120 c g t \sqrt{2} \cdot 2 - 3 \sqrt{2}}{2}$

Step 6

Multiply $2$ by $120$ .

$\frac{240 c g t \sqrt{2} - 3 \sqrt{2}}{2}$