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eimsori [14]
3 years ago
14

What is the value of x?

Mathematics
1 answer:
Lesechka [4]3 years ago
6 0

Answer:

Step-by-step explanation:

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Please please help!!
shepuryov [24]

Answer:

\large\boxed{x=0\ and\ x=\pi}

Step-by-step explanation:

\tan^2x\sec^2x+2\sec^2x-\tan^2x=2\\\\\text{Use}\ \tan x=\dfrac{\sin x}{\cos x},\ \sec x=\dfrac{1}{\cos x}:\\\\\left(\dfrac{\sin x}{\cos x}\right)^2\left(\dfrac{1}{\cos x}\right)^2+2\left(\dfrac{1}{\cos x}\right)^2-\left(\dfrac{\sin x}{\cos x}\right)^2=2\\\\\left(\dfrac{\sin^2x}{\cos^2x}\right)\left(\dfrac{1}{\cos^2x}\right)+\dfrac{2}{\cos^2x}-\dfrac{\sin^2x}{\cos^2x}=2

\dfrac{\sin^2x}{(\cos^2x)^2}+\dfrac{2-\sin^2x}{\cos^2x}=2\\\\\text{Use}\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-(1-\cos^2x)}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{2-1+\cos^2x}{\cos^2x}=2\\\\\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{1+\cos^2x}{\cos^2x}=2

\dfrac{1-\cos^2x}{(\cos^2x)^2}+\dfrac{(1+\cos^2x)(\cos^2x)}{(\cos^2x)^2}=2\qquad\text{Use the distributive property}\\\\\dfrac{1-\cos^2x+\cos^2x+\cos^4x}{\cos^4x}=2\\\\\dfrac{1+\cos^4x}{\cos^4x}=2\qquad\text{multiply both sides by}\ \cos^4x\neq0\\\\1+\cos^4x=2\cos^4x\qquad\text{subtract}\ \cos^4x\ \text{from both sides}\\\\1=\cos^4x\iff \cos x=\pm\sqrt1\to\cos x=\pm1\\\\ x=k\pi\ for\ k\in\mathbb{Z}\\\\\text{On the interval}\ 0\leq x

4 0
2 years ago
18) What value of x makes R(x) = 10
Illusion [34]
<h3>Two Answers:  <u>x = 2 and x = 10</u></h3>

========================================================

Explanation:

Draw a horizontal line through 10 on the y axis. This is because R(x) = 10 is the same as y = 10. The output of the function is the y value.

See the diagram below.

The horizontal line crosses the parabola at two locations. From those points, draw a vertical line straight down to the x axis. Note how we land at x = 2 and x = 10. This means that R(2) = 10 and R(10) = 10.

8 0
3 years ago
If your chances of losing the shell game if you randomly pick is 2 in 3. What are the chances that you would lose 5 games in a r
NISA [10]

Answer:

c

Step-by-step explanation:

4 0
2 years ago
Complete the Area Model that would be used to multiply<br><br><br><img src="https://tex.z-dn.net/?f=3x%28x%5E2%2B4x%2B5%29" id="
lianna [129]

Answer:

A triangle is shown Below based on this triangle which one of the following statements is true

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
The reflection of the point (4, 6) over the y-axis is:
Brums [2.3K]
(-4,6)
The x value changes bc since it is a reflection y cannot change and x becomes negative
8 0
2 years ago
Read 2 more answers
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