Find the Exact Value (4sin(45)cos(45))/(tan(30)cot(30))

Solve Math

Trigonometry

$\frac{4 \sin (45) \cos (45)}{\tan (30) \cot (30)}$

Simplify the numerator.

Tap for more steps...

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

$\frac{4 \frac{\sqrt{2}}{2} \cos (45)}{\tan (30) \cot (30)}$

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

$\frac{4 \frac{\sqrt{2}}{2} \frac{\sqrt{2}}{2}}{\tan (30) \cot (30)}$

Combine exponents.

Tap for more steps...

Combine $4$ and $\frac{\sqrt{2}}{2}$ .

$\frac{\frac{4 \sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2}}{\tan (30) \cot (30)}$

Multiply $\frac{4 \sqrt{2}}{2}$ and $\frac{\sqrt{2}}{2}$ .

$\frac{\frac{4 \sqrt{2} \sqrt{2}}{2 \cdot 2}}{\tan (30) \cot (30)}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{\frac{4 ({\sqrt{2}}^{1} \sqrt{2})}{2 \cdot 2}}{\tan (30) \cot (30)}$

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{\frac{4 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{2 \cdot 2}}{\tan (30) \cot (30)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\frac{4 {\sqrt{2}}^{1 + 1}}{2 \cdot 2}}{\tan (30) \cot (30)}$

Add $1$ and $1$ .

$\frac{\frac{4 {\sqrt{2}}^{2}}{2 \cdot 2}}{\tan (30) \cot (30)}$

Multiply $2$ by $2$ .

$\frac{\frac{4 {\sqrt{2}}^{2}}{4}}{\tan (30) \cot (30)}$

Reduce the expression by cancelling the common factors.

Tap for more steps...

Reduce the expression $\frac{4 {\sqrt{2}}^{2}}{4}$ by cancelling the common factors.

Tap for more steps...

Cancel the common factor.

$\frac{\frac{4 {\sqrt{2}}^{2}}{4}}{\tan (30) \cot (30)}$

Rewrite the expression.

$\frac{\frac{{\sqrt{2}}^{2}}{1}}{\tan (30) \cot (30)}$

Divide ${\sqrt{2}}^{2}$ by $1$ .

$\frac{{\sqrt{2}}^{2}}{\tan (30) \cot (30)}$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Tap for more steps...

Rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\frac{{(2^{\frac{1}{2}})}^{2}}{\tan (30) \cot (30)}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2^{\frac{1}{2} \cdot 2}}{\tan (30) \cot (30)}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2^{\frac{2}{2}}}{\tan (30) \cot (30)}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\frac{2^{\frac{2}{2}}}{\tan (30) \cot (30)}$

Divide $1$ by $1$ .

$\frac{2^{1}}{\tan (30) \cot (30)}$

Evaluate the exponent.

$\frac{2}{\tan (30) \cot (30)}$

Simplify the denominator.

Tap for more steps...

The exact value of $\tan (30)$ is $\frac{\sqrt{3}}{3}$ .

$\frac{2}{\frac{\sqrt{3}}{3} \cot (30)}$

The exact value of $\cot (30)$ is $\sqrt{3}$ .

$\frac{2}{\frac{\sqrt{3}}{3} \sqrt{3}}$

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

$\frac{2}{\frac{\sqrt{3} \sqrt{3}}{3}}$

Simplify the numerator.

Tap for more steps...

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{2}{\frac{{\sqrt{3}}^{1} \sqrt{3}}{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{2}{\frac{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2}{\frac{{\sqrt{3}}^{1 + 1}}{3}}$

Add $1$ and $1$ .

$\frac{2}{\frac{{\sqrt{3}}^{2}}{3}}$

Simplify by cancelling exponent with radical.

Tap for more steps...

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{2}{\frac{{(3^{\frac{1}{2}})}^{2}}{3}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2}{\frac{3^{\frac{1}{2} \cdot 2}}{3}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2}{\frac{3^{\frac{2}{2}}}{3}}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$\frac{2}{\frac{3^{\frac{2}{2}}}{3}}$

Divide $1$ by $1$ .

$\frac{2}{\frac{3^{1}}{3}}$

Evaluate the exponent.

$\frac{2}{\frac{3}{3}}$

Simplify the expression.

Tap for more steps...

Divide $3$ by $3$ .

$\frac{2}{1}$

Divide $2$ by $1$ .

$2$

Do you know how to Find the Exact Value (4sin(45)cos(45))/(tan(30)cot(30))? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	nine hundred thirty-one million nine hundred twenty thousand three hundred eight

Interesting facts

931920308 has 32 divisors, whose sum is 2288437920
The reverse of 931920308 is 803029139
Previous prime number is 4973

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 35
Digital Root 8

Name

Name	two billion sixty-nine million eight hundred eighteen thousand two hundred sixty-eight

Interesting facts

2069818268 has 32 divisors, whose sum is 5334436224
The reverse of 2069818268 is 8628189602
Previous prime number is 443

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 50
Digital Root 5

Name

Name	one billion one hundred forty-seven million eight hundred fifty-seven thousand five hundred fifty-three

Interesting facts

1147857553 has 8 divisors, whose sum is 1187092736
The reverse of 1147857553 is 3557587411
Previous prime number is 541

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 46
Digital Root 1

Simplify sin(-300)

Solve the Triangle sin(theta)=1/2

Simplify cot(25)

Solve for x log base 20 of -2x+7 = log base 20 of 2x-1

Simplify ((t+1)(t^2-1))/((t-1)(t+1)^2)