Expand Using Sum/Difference Formulas cos(60 degrees -45 degrees )

$\cos (60 ° - 45 °)$

Use the difference formula for cosine to simplify the expression. The formula states that $\cos (A - B) = \cos (A) \cos (B) + \sin (A) \sin (B)$ .

$\cos (60 °) \cdot \cos (45 °) + \sin (60 °) \cdot \sin (45 °)$

Remove parentheses.

$\cos (60 °) \cdot \cos (45 °) + \sin (60 °) \cdot \sin (45 °)$

Simplify each term.

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

$\frac{1}{2} \cdot \cos (45 °) + \sin (60 °) \cdot \sin (45 °)$

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

$\frac{1}{2} \cdot \frac{\sqrt{2}}{2} + \sin (60 °) \cdot \sin (45 °)$

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

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Multiply $\frac{1}{2}$ and $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2 \cdot 2} + \sin (60 °) \cdot \sin (45 °)$

Multiply $2$ by $2$ .

$\frac{\sqrt{2}}{4} + \sin (60 °) \cdot \sin (45 °)$

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

$\frac{\sqrt{2}}{4} + \frac{\sqrt{3}}{2} \cdot \sin (45 °)$

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

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

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

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

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

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

$\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}$

Combine the numerators over the common denominator.

$\frac{\sqrt{2} + \sqrt{6}}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2} + \sqrt{6}}{4}$

Decimal Form:

$0.96592582 \dots$

Do you know how to Expand Using Sum/Difference Formulas cos(60 degrees -45 degrees )? 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	four hundred twenty-three million nine hundred seventy-two thousand six hundred ninety-eight

Interesting facts

423972698 has 4 divisors, whose sum is 635959050
The reverse of 423972698 is 896279324
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 50
Digital Root 5

Name

Name	one billion nine hundred fifty million five hundred twelve thousand seven hundred fifty-two

Interesting facts

1950512752 has 64 divisors, whose sum is 9876754440
The reverse of 1950512752 is 2572150591
Previous prime number is 5333

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 37
Digital Root 1

Name

Name	one billion five hundred sixty-one million sixty-seven thousand four hundred sixty-nine

Interesting facts

1561067469 has 4 divisors, whose sum is 1574410044
The reverse of 1561067469 is 9647601651
Previous prime number is 117

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 45
Digital Root 9

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