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aniked [119]
3 years ago
8

Find an exact value. Cos 75° negative square root of six plus square root of two quantity square root of six minus square root o

f two divided by four quantity negative square root of six plus square root of two divided by four square root of six minus square root of two
Mathematics
1 answer:
ehidna [41]3 years ago
6 0

Answer:

√2(√3 - 1)/4

Step-by-step explanation:

To find an exact value for Cos75°, we use the compound angle formula. Since 75° = 45° + 30°, Cos75° = Cos(45° + 30°).

Using Cos(A + B) = CosACosB - SinASinB where A = 45° and B = 30°,  

Cos75° = Cos(45° + 30°) = Cos45°Cos30° - Sin45°Sin30°

Now Cos45° = Sin45° = 1/√2 = √2/2, Cos30° = √3/2 and Sin30° = 1/2.

Substituting these values into the above equation, we have

Cos75° = Cos(45° + 30°)

= Cos45°Cos30° - Sin45°Sin30°

= √2/2 × √3/2 -  √2/2 × 1/2

= √6/4 -√2/4

= √2(√3 - 1)/4

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cricket20 [7]

You can observe that angle 1 and angle with 47° are inside a parallelogram.

Consider that the sum of the internal angles of a parallelogram is 360°.

Moreover, consider that the angle at the top right of the parallogram is congruent with the angle of 47°, then, such an angle is if 47°.

Consider that angle down right side is congruent with angle 1, then, they have the same measure.

You can write the previous situation in the following equation:

47 + 47 + ∠1 + ∠1 = 360 simplify like terms

94 + 2∠1 = 360 subtract both sides by 94

2∠1 = 360 - 94

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6 0
1 year ago
What is the quotient? Negative StartFraction 3 over 8 EndFraction divided by negative one-fourth
anyanavicka [17]

Answer:

\dfrac{3}{2}

Step-by-step explanation:

We are given 2 fractions.

1st fraction is Negative StartFraction 3 over 8

i.e.

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2nd fraction is negative one-fourth

i.e.

-\dfrac{1}{4}

We have to find the quotient when 1st fraction is divided by 2nd fraction.

<u>Definition</u> of quotient is given as:

Quotient is the result obtained when one number is divided by other number.

-\dfrac{3}{8} \div -\dfrac{1}{4} \text{ is to be calculated.}

\div is converted to \times and the 2nd fraction is reversed i.e.

if the fraction is \frac{p}{q} it becomes \frac{q}{p} and the sign \div is changed to \times.

Solving above:

-\dfrac{3}{8} \times -\dfrac{4}{1}\\ \text {Multiplication/Division of 2 negative number gives a positive number}\\\Rightarrow \dfrac{3}{2}

So, the quotient is \frac{3}{2}.

6 0
3 years ago
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andrew-mc [135]

A

the word 'of' means to multiply

0.45 × 80 = 36


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Step-by-step explanation:

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3 years ago
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Step-by-step explanation:

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