What is the slope of the line passing through the points (1, −5)(1, −5) and (4, 1)(4, 1)?

Complete the identity.<br> 1) sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?

Alecsey [184]

Answer:

See Explanation

Step-by-step explanation:

<em>Question like this are better answered if there are list of options; However, I'll simplify as far as the expression can be simplified</em>

Given

$sec^4 x + sec^2 x tan^2 x - 2 tan^4 x$

Required

Simplify

$(sec^2 x)^2 + sec^2 x tan^2 x - 2 (tan^2 x)^2$

Represent $sec^2x$ with a

Represent $tan^2x$ with b

The expression becomes

$a^2 + ab- 2 b^2$

Factorize

$a^2 + 2ab -ab- 2 b^2$

$a(a + 2b) -b(a+ 2 b)$

$(a -b) (a+ 2 b)$

Recall that

$a = sec^2x$

$b = tan^2x$

The expression $(a -b) (a+ 2 b)$ becomes

$(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

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

In trigonometry

$sec^2x =1 +tan^2x$

Subtract $tan^2x$ from both sides

$sec^2x - tan^2x =1 +tan^2x - tan^2x$

$sec^2x - tan^2x =1$

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

Substitute 1 for $sec^2x - tan^2x$ in $(sec^2x -tan^2x) (sec^2x+ 2 tan^2x)$

$(1) (sec^2x+ 2 tan^2x)$

Open Bracket

$sec^2x+ 2 tan^2x$ ------------------This is an equivalence

$(secx)^2+ 2 (tanx)^2$

Solving further;

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

In trigonometry

$secx = \frac{1}{cosx}$

$tanx = \frac{sinx}{cosx}$

Substitute the expressions for secx and tanx

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

$(secx)^2+ 2 (tanx)^2$ becomes

$(\frac{1}{cosx})^2+ 2 (\frac{sinx}{cosx})^2$

Open bracket

$\frac{1}{cos^2x}+ 2 (\frac{sin^2x}{cos^2x})$

$\frac{1}{cos^2x}+ \frac{2sin^2x}{cos^2x}$

Add Fraction

$\frac{1 + 2sin^2x}{cos^2x}$ ------------------------ This is another equivalence

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

In trigonometry

$sin^2x + cos^2x= 1$

Make $sin^2x$ the subject of formula

$sin^2x= 1 - cos^2x$

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Substitute the expressions for $1 - cos^2x$ for $sin^2x$

$\frac{1 + 2(1 - cos^2x)}{cos^2x}$

Open bracket

$\frac{1 + 2 - 2cos^2x}{cos^2x}$

$\frac{3 - 2cos^2x}{cos^2x}$ ---------------------- This is another equivalence

8 0

3 years ago

What is the range of the function: {(1, 3); (3, 5); (5, 7); (7, 9)}? A. {1, 3, 5, 7}

IRISSAK [1]

$\{(1;\ \underline{3});\ (3;\ \underline{5});\ (5;\ \underline{7});\ (7;\ \underline{9})\}\\\\Range\ of\ this\ function:\{3;\ 5;\ 7;\ 9\}\\\\Domain\ of\ this\ function:\{1;\ 3;\ 5;\ 7\}$

5 0

3 years ago

Read 2 more answers

Find the equation of the line that contains the point (3,9) and is parallel to the line y=4x+1. Write the line in slope-intercep

Aleksandr-060686 [28]

Y = 4x + 1....slope here is 4. A parallel line will have the same slope

y = mx + b
slope(m) = 4
(3,9)...x = 3 and y = 9
now we sub and find b, the y int
9 = 4(3) + b
9 = 12 + b
9 - 12 = b
-3 = b

so ur parallel equation is : y = 4x - 3

5 0

3 years ago

What are the possible steps involved in solving the equation shown? Select three options. 3.5 + 1.2(6.3 – 7x) = 9.38 Add 3.5 and

motikmotik

Answer:

1) Distribute 1.2 to 6.3 and -7x

2)Combine 3.5 and 7.56

3)Subtract 11.06 from both sides

Step-by-step explanation:

3.5 + 1.2(6.3 - 7x) = 9.38

Distribute 1.2 to 6.3 and -7x

3.5 + 1.2* 6.3 - 1.2 * 7x = 9.38

3.5 + 7.56 - 8.4x = 9.38

Combine 3.5 and 7.56

11.06 - 8.4x = 9.38

Subtract 11.06 from both sides

11.06 - 8.4x -11.06 = 9.38 - 11.06

-8.4x = -1.68

To find solution:

Divide both sides by (-8.4)

-8.4x/-8.4 = -1.68/-8.4

x = 0.02

8 0

3 years ago

Read 2 more answers

I need help solving for the angle.

ohaa [14]

Use a protracter :) hope this helps!

6 0

3 years ago