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2 years ago

Look at the system of equations below.

Mathematics

1 answer:

MakcuM [25]2 years ago

6 0

Answer:

Step-by-step explanation:

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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

Tara earns $9 for each dog she walks. She walks 10 dogs an hour. After walking dogs for 4 hours, how much money will Tara have e

solong [7]

Answer: $360

Step-by-step explanation:

In one hour, she makes $9 * 10 dogs = $90.

In 4 hours, we simply multiply that by 4 to get $90 * 4 = $360 total

4 0

2 years ago

Read 2 more answers

what is the equation of the following line? Be sure to scroll down first to see all answer options. ( -1/2, -3) ( 0, 0)

dlinn [17]

I got y = 1/5x fo this one.............

5 0

3 years ago

Read 2 more answers

(7) Explain why 198: 1,287 and 2: 13 are equivalent ratios. Your answer I

ladessa [460]

Answer:

Because they are both multiplied.

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

........................

shtirl [24]

Answer:

Step-by-step explanation:

Figure (1)

x° = 107° [Vertically opposite angles]

Since, vertical angles are equal in measure.

Figure (2)

x + 71° = 90° [Given, complementary angles]

x = 90° - 71°

x = 19°

Figure (3)

x + 21° = 180° [Given as supplementary angles]

x = 180° - 21°

x = 159°

Figure (4)

x = 129° [Vertical angles]

Figure (5)

x° = 90° [Given]

z° + 34° = 90°

z° = 90° - 34°

z° = 56°

Since, x° + y° + z° = 180° [Linear angles]

90° + y° + 56° = 180°

y° + 146° = 180°

y° = 180° - 146°

y° = 34°

7 0

2 years ago