David drove 135 miles in 3 hours

Solve cos(2x)=1-sin(x)

Vedmedyk [2.9K]

Given:

$cos(2x)=1-sin(x)$

Expanding using double angle formula,

$1 - 2 \sin^{2} (x) = 1 - \sin(x)$

Rearranging into a single equation,

$1 - 2 \sin^{2}(x) - 1 + \sin(x) = 0$

Combining like terms,

$- 2 \sin^{2} (x) + \sin(x) = 0$

Now multiplying each term by -1,

$2 \sin^{2} (x) - \sin(x) = 0$

Factor greatest common factors out,

$\sin(x)(2 \sin(x) - 1) = 0$

Applying Zero property rule,

$\sin(x) = 0 \: or \: 2 \sin(x) - 1 = 0$

• Solve the trignometric equation to find a particular solution,

$x = 0 \: or \: x = π$

$= > x = 2nπ \: or \: x = π + 2nπ$

• Find the union of the solution sets,

$x = nπ$ }

• Rearrange unknown terms to the left side,

$2 \sin(x) = 1$

• Divide both sides of the equation by the coefficient of variable,

$\sin(x) = \frac{1}{2}$

• Solve the trignometric equation to find a particular solution,

$x = \frac{π}{6} \: or \: x = \frac{5π}{6}$

$= > x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

}

☆ Now finding the union of both sets

$x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

Hence, the answer is $x = nπ \: or \: x = \frac{π}{6} + 2nπ \: or \: x = \frac{5π}{6} + 2nπ,n∈Z$

3 0

3 years ago

Emery earns money mowing his neighbors' lawns. He charges $1.25 per square yard for each lawn he mows. His neighbors, the Flores

aleksandr82 [10.1K]

Answer: 4.2 yards

Step-by-step explanation:

Let x = length of the Flores' lawn in yards.

Then, Area of lawn = 4x sq. yard [Area of rectangle = width x length , here width = 4 yds (given)]

Charge per square yard = $1.25

Charge for Flores lawn = 1.25 × (Area of lawn)

= 1.25 (4x)

= 5x

As per given,

$5x=21\\\\\Rightarrow\ x=\dfrac{21}{5}\\\\\Rightarrow\ x=4.2$

Hence, the length of the Flores's lawn = 4.2 yards

5 0

3 years ago

331 X 46=what is ittttt oooof

Nata [24]

Step-by-step explanation:

(331)(46)

=15226

6 0

4 years ago

Read 2 more answers

Question 10. Simplify the expression. (x^2 - 9)/(x^2 + 2x - 15)

krek1111 [17]

So the right ans is of option B.

Look at the attached picture ⤴

Hope it will help u...

3 0

3 years ago

2. A record store is going out of business and sold any

liubo4ka [24]

Answer:

A) c + CD = 20

B) 6c + 12CD = 192

Multiplying equation A by -6 we get:

A) -6c -6CD = -120

B) 6c + 12 CD = 192

Adding the equations we get

0 + 6 CD = 72

There are 12 CD's and

c + 12 = 20

There are 8 cassettes

Step-by-step explanation:

7 0

2 years ago