Evaluate (sin(60 degrees ))(cos(30 degrees ))+(cos(60 degrees ))(sin(30 degrees ))

$(\sin (60 °)) (\cos (30 °)) + (\cos (60 °)) (\sin (30 °))$

Simplify each term.

The exact value of $\sin (60 °)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2} \cos (30 °) + (\cos (60 °)) (\sin (30 °))$

The exact value of $\cos (30 °)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} + (\cos (60 °)) (\sin (30 °))$

Multiply $\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}$ .

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3} \sqrt{3}}{2 \cdot 2} + (\cos (60 °)) (\sin (30 °))$

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

$\frac{{\sqrt{3}}^{1} \sqrt{3}}{2 \cdot 2} + (\cos (60 °)) (\sin (30 °))$

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

$\frac{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}{2 \cdot 2} + (\cos (60 °)) (\sin (30 °))$

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

$\frac{{\sqrt{3}}^{1 + 1}}{2 \cdot 2} + (\cos (60 °)) (\sin (30 °))$

Add $1$ and $1$ .

$\frac{{\sqrt{3}}^{2}}{2 \cdot 2} + (\cos (60 °)) (\sin (30 °))$

Multiply $2$ by $2$ .

$\frac{{\sqrt{3}}^{2}}{4} + (\cos (60 °)) (\sin (30 °))$

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{{(3^{\frac{1}{2}})}^{2}}{4} + (\cos (60 °)) (\sin (30 °))$

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

$\frac{3^{\frac{1}{2} \cdot 2}}{4} + (\cos (60 °)) (\sin (30 °))$

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

$\frac{3^{\frac{2}{2}}}{4} + (\cos (60 °)) (\sin (30 °))$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3^{\frac{2}{2}}}{4} + (\cos (60 °)) (\sin (30 °))$

Rewrite the expression.

$\frac{3^{1}}{4} + (\cos (60 °)) (\sin (30 °))$

Evaluate the exponent.

$\frac{3}{4} + (\cos (60 °)) (\sin (30 °))$

The exact value of $\cos (60 °)$ is $\frac{1}{2}$ .

$\frac{3}{4} + \frac{1}{2} \sin (30 °)$

The exact value of $\sin (30 °)$ is $\frac{1}{2}$ .

$\frac{3}{4} + \frac{1}{2} \cdot \frac{1}{2}$

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$\frac{3}{4} + \frac{1}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{3}{4} + \frac{1}{4}$

Combine fractions.

Combine the numerators over the common denominator.

$\frac{3 + 1}{4}$

Simplify the expression.

Add $3$ and $1$ .

$\frac{4}{4}$

Divide $4$ by $4$ .

$1$

Evaluate (sin(60 degrees ))(cos(30 degrees ))+(cos(60 degrees ))(sin(30 degrees ))

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