Find the difference:

If sinA=√3-1/2√2,then prove that cos2A=√3/2 prove that

Ivan

Answer:

$\boxed{\sf cos2A =\dfrac{\sqrt3}{2}}$

Step-by-step explanation:

Here we are given that the value of sinA is √3-1/2√2 , and we need to prove that the value of cos2A is √3/2 .

Given :-

• $\sf\implies sinA =\dfrac{\sqrt3-1}{2\sqrt2}$

To Prove :-

• $\sf\implies cos2A =\dfrac{\sqrt3}{2}$

Proof :-

We know that ,

$\sf\implies cos2A = 1 - 2sin^2A$

Therefore , here substituting the value of sinA , we have ,

$\sf\implies cos2A = 1 - 2\bigg( \dfrac{\sqrt3-1}{2\sqrt2}\bigg)^2$

Simplify the whole square ,

$\sf\implies cos2A = 1 -2\times \dfrac{ 3 +1-2\sqrt3}{8}$

Add the numbers in numerator ,

$\sf\implies cos2A = 1-2\times \dfrac{4-2\sqrt3}{8}$

Multiply it by 2 ,

$\sf\implies cos2A = 1 - \dfrac{ 4-2\sqrt3}{4}$

Take out 2 common from the numerator ,

$\sf\implies cos2A = 1-\dfrac{2(2-\sqrt3)}{4}$

Simplify ,

$\sf\implies cos2A = 1 -\dfrac{ 2-\sqrt3}{2}$

Subtract the numbers ,

$\sf\implies cos2A = \dfrac{ 2-2+\sqrt3}{2}$

Simplify,

$\sf\implies \boxed{\pink{\sf cos2A =\dfrac{\sqrt3}{2}} }$

Hence Proved !

8 0

2 years ago

David is making patterns using these rules. Rule for Pattern A: start with 20 and subtract 2 Rule for Pattern B: start with 10 a

pochemuha

Answer:

20,18,16,14,12,10,8,6,4,2

10,9,8,7,6,5,4,3,2,1

Step-by-step explanation:

Pattern A:

Rule : start with 20 and subtract 2

Pattern B:

Rule : Start with 10 and subtract 1

Pattern 1:

20 - 2 = 18

18 - 2 = 16

16 - 2 = 14

14 - 2 = 12

12 - 2 = 10

10 - 2 = 8

8 - 2 = 6

6 - 2 = 4

4 - 2 = 2

20,18,16,14,12,10,8,6,4,2

Pattern 2:

10 - 1 = 9

9 - 1 = 8

8 - 1 = 7

7 - 1 = 6

6 - 1 = 5

5 - 1 = 4

4 - 1 = 3

3 - 1 = 2

2 - 1 = 1

10,9,8,7,6,5,4,3,2,1

5 0

2 years ago

What is the surface area of a storage box that measures 15 centimeters by 12 centimeters by 8 centimeters?

Leya [2.2K]

L = 15
w = 12
h = 8

Surface Area = 2(lw + wh + lh)
S.A. = 2(15*12 + 12*8 + 15*8)
S.A. = 2(180 + 96 + 120)
S.A. = 2(396)
S.A. = 792 cm^2

7 0

2 years ago

The ratio of 1.4/7 in the simplest form

sweet [91]

If you want to convert 1.4 into a fraction, you can do it like this:

1 equals to 1/1 and 0.4 equals to 4/10 which simplifies to 2/5.
The result is 1 2/5.

If you want to write the ratio of 1.4/7 in the simplest form, you can do this using the following steps:

1.4/7 = 1 2/5 / 7 = 7/5 / 7 = 7/5 * 1/7 = 1/5 = 0.2

The correct result would be 1/5.

3 0

2 years ago

I need help getting this answer right hurry

Rus_ich [418]

Answer:

Bring over -1 to get m = 10

Step-by-step explanation:

4 0

2 years ago

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