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3 years ago

Verify the identity. tan x plus pi divided by two = -cot x

1 answer:

7 0

Recall that sin(π/2) = 1, and cos(π/2) = 0,

$\bf \textit{Sum and Difference Identities}
\\\\
sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)
\\\\
sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)
\\\\
cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)
\\\\
cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\
-------------------------------\\\\
$

$\bf tan\left(x+\frac{\pi }{2} \right)=-cot(x)\\\\
-------------------------------\\\\
tan\left(x+\frac{\pi }{2} \right)\implies \cfrac{sin\left(x+\frac{\pi }{2} \right)}{cos\left(x+\frac{\pi }{2} \right)}
\\\\\\
\cfrac{sin(x)cos\left(\frac{\pi }{2} \right)+cos(x)sin\left(\frac{\pi }{2} \right)}{cos(x)cos\left(\frac{\pi }{2} \right)-sin(x)sin\left(\frac{\pi }{2} \right)}\implies \cfrac{sin(x)\cdot 0~~+~~cos(x)\cdot 1}{cos(x)\cdot 0~~-~~sin(x)\cdot 1}
\\\\\\
\cfrac{cos(x)}{-sin(x)}\implies -cot(x)$

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What is 800 divided by 1000

Monica [59]

Answer:

Erm idk what you meant but the answers either 0.8 or .125

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3 years ago

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Aloiza [94]

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3 years ago

The equation of line m is 3x−5y=−4

vaieri [72.5K]

Slope of this line, -5y = -3x - 4
y = 3/5x + 4/5
So, slope of line which is perpendicular = -5/3 [reciprocal & opposite ]

In short, Your Answer would be -5/3

Hope this helps!

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3 years ago

2/7m-1/7=3/14 solve step by step

yulyashka [42]

Solution for $\frac{2}{7}m - \frac{1}{7} = \frac{3}{14} \ is \ m = \frac{5}{4} \ or \ m = 1\frac{1}{4} \ or \ m = 1.25$

<h3>Further explanation</h3>

It is a case about one variable linear quations and we have to solve the equation to get the variable m. There are two ways to solve it!

Our main plan is to isolate the variable m alone at the end of the process on one side of the equation until the variable will be equal to the value on the opposite side.

<u>First way</u>

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

Let us add $\frac{1}{7}$ to both sides

$\frac{2}{7}m - \frac{1}{7} + \frac{1}{7} = \frac{3}{14} + \frac{1}{7}$

$\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}$

On the right side for the addition operation, we equate the common denominator by multiplying $\ \frac{1}{7} \ by \ \frac{2}{2}$

$\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}$

Then we combine terms to get

$\frac{2}{7}m = \frac{5}{14}$

Divide by the coefficient of m, or in other words, multiply both sides by $\frac{7}{2}$

$\frac{2}{7}m \times \frac{7}{2} = \frac{5}{14} \times \frac{7}{2}$

Finally, the solution is obtained as follows

$m = \frac{35}{28}$

Simplify fractions, both the numerator and denominator are divided equally by 7.

$\boxed{ \ m = \frac{5}{4} \ }$

Convert into mixed fractions, we get:

$\boxed{ \ m = 1 \frac{1}{4} \ }$

In decimal form, we get

$m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

<u>Second way (a quick way)</u>

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

Because the denominators 7 and 14 have LCM = 14, both sides are multiplied by 14 (LCM is the Least Common Multiple)

$14 \times \big( \frac{2}{7}m - \frac{1}{7} \big) = 14\times \big( \frac{3}{14} \big)$

We use the distributive property of multiplication on the left side

$\frac{28}{7}m - \frac{14}{7} = \frac{42}{14}$

or it can also directly lead to

$4m - 2 = 3$

Add 2 to both sides, we get

$4m = 5$

Divide by the coefficient of m, or in other words, both sides are divided by 4

$\boxed{ \ m = \frac{5}{4} \ }$

Or, $\boxed{ \ m = 1 \frac{1}{4} \ }$

Or, $m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

Wanna check the solution into the equation?

$\big( \frac{2}{7} \times \frac{5}{4} \big) - \frac{1}{7} = \frac{3}{14}$

$\frac{10}{28} - \frac{1}{7} = \frac{3}{14}$

$\frac{5}{14} - \frac{2}{14} = \frac{3}{14}$

$\frac{3}{14} = \frac{3}{14}$

Both sides show the same value, so the solution is correct.

Note:

Remember, how to manipulate both sides of the equation with the algebraic properties of equality such as:

adding,
subtracting,
multiplying, and/or
dividing both sides of the equation with the same number.

In the form of fractions, the steps that must be considered are

equate the denominator,
simplify fractions, and
for the final answer, convert fractions to mixed fractions or decimal forms

All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation.

<h3>Learn more</h3>

A word problem that forms a single variable linear equation brainly.com/question/1566971
Learn more about the single variable linear equation that has no solution, has one solution, and has infinitely many solutions brainly.com/question/2595790
Questioning the stages of solving a word problem about one variable linear equations brainly.com/question/2038876

<h3>Answer details </h3>

Grade : Middle School

Subject : Mathematics

Chapter : Linear Equation in One Variable

Keywords : solve, solution, variable, coefficient, 2/7m - 1/7 = 3/14, 5/4, 1 1/4, 1.125, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, subtract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal

4 0

3 years ago

Read 2 more answers

The figure is made from squares of different sizes.Find the area of A if the side of each of the two indentical smallest square

Temka [501]

Answer:

The area of square A is 256 cm²

Step-by-step explanation:

<em>The four sides of a square are equal in length</em>
<em>Area of a square = side × side</em>

In the given figure

∵ The sides of the square E = 2 cm each

∵ The sides of the square F = 2 cm each

∵ The side of square D is the sum of the sides of squares E and F

∴ The sides of the square D = 2 + 2 = 4 cm each

∵ The side of square C is the sum of the sides of squares E and D

∴ The sides of square C = 2 + 4 = 6 cm each

∵ The side of square B is the sum of the sides of squares C, E, and F

∴ The sides of square B = 6 + 2 + 2= 10 cm each

∵ The side of square A is the sum of the sides of squares B, F, and D

∴ The sides of square A = 10 + 2 + 4= 16 cm each

∵ Area of square A = side × side

∴ Area of square A = 16 × 16

∴ Area of square A = 256 cm²

∴ The area of square A is 256 cm²

3 0

2 years ago