If m∠Q = (3x+5)° and m∠C = 55°, then x=

1-cot^2a+cot^4a=sin^2a(1+cot^6a) prove it.

aliina [53]

Step-by-step explanation:

We have

1-cot²a + cot⁴a = sin²a(1+cot⁶a)

First, we can take a look at the right side. It expands to sin²a + cot⁶(a)sin²(a) = sin²a + cos⁶a/sin⁴a (this is the expanded right side) as cot(a) = cos(a)/sin(a), so cos⁶a = cos⁶a/sin⁶a. Therefore, it might be helpful to put everything in terms of sine and cosine to solve this.

We know 1 = sin²a+cos²a and cot(a) = cos(a)/sin(a), so we have

1-cot²a + cot⁴a = sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

Next, we know that in the expanded right side, we have sin²a + something. We can use that to isolate the sin²a. The rest of the expanded right side has a denominator of sin⁴a, so we can make everything else have that denominator.

sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

= sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

We can then factor cos²a out of the numerator

sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

= sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

Then, in the expanded right side, we can notice that the fraction has a numerator with only cos in it. We can therefore write sin⁴a in terms of cos (we don't want to write the sin²a term in terms of cos because it can easily add with cos²a to become 1, so we can hold that off for later) , so

sin²a = (1-cos²a)

sin⁴a = (1-cos²a)² = cos⁴a - 2cos²a + 1

sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-2cos²a+1-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

factor our the -cos²a-sin²a as -1(cos²a+sin²a) = -1(1) = -1

sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

= sin²a + cos²a (cos⁴a-1 + 1)/sin⁴a

= sin²a + cos⁶a/sin⁴a

= sin²a(1+cos⁶a/sin⁶a)

= sin²a(1+cot⁶a)

8 0

3 years ago

What is the answer lol somebody help me please and thank you !

PilotLPTM [1.2K]

I'm guessing that you know about 45-45-90 and 30-60-90 triangles.

In 45-45-90 triangles, the legs are in a ratio such that the hypotenuse is $\sqrt{2}$ times the legs.

In 30-60-90 triangles, the legs are in a ratio of 1: $\sqrt{3}$ :2

In the picture given we have been given a value of the side of the 45-45-90 triangle. We can deduce that the value of the hypotenuse is 9 $\sqrt{2}$ because of the ratio of the sides of a 45-45-90 triangle.

The 30-60-90 triangle shares the same hypotenuse, and so we now know a value of one of its sides as well. The ratio of the side of value 'x' and the hypotenuse is $\sqrt{3}$ : 2

We can create an equation to solve for x using these ratios:

$\frac{\sqrt{3} }{2}$ = $\frac{x}{9\sqrt{2} }$

Cross multiply:

2x = 9 $\sqrt{6}$

x = $\frac{9\sqrt{6} }{2}$

Option C

4 0

3 years ago

Peter is in the school play.his teacher gave 1 copy of the play to each of 6 students.how many copies of the play did the teache

Dmitrij [34]

The teacher handed out 6 copies

4 0

4 years ago

Read 2 more answers

Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of

kaheart [24]

Answer:

$45\pi$ square inches$

Step-by-step explanation:

The radius, r of the expanding circle of oil is modeled by the function:

$r=3\sqrt{s}$ , where s is time in seconds.

When s=5

Radius $r(5)=3\sqrt{5}$ inches$

Area of a circle $=\pi r^2$

Therefore, the area of the oil spill when s=5 seconds

$=\pi* (3\sqrt{5})^2\\=45\pi$ square inches$

The area of the spill when s=5 seconds is 45pi square inches.

6 0

3 years ago

What is 2 49/100 as a decimal number?

Alchen [17]

2 49/100 in decimal form is 2.49 because a decimal in the one hundredths would be like this: 0.09 or 0.49, and the two is a whole number, so it would go before the decimal like this: 2.09 or 2.49.

Hope this helped:):)

4 0

4 years ago