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ExtremeBDS [4]
3 years ago
12

Prove the identity

Mathematics
1 answer:
Troyanec [42]3 years ago
3 0

Answer:

Proved

Step-by-step explanation:

The options are not given. So, I will solve from scratch

Given

\frac{secx-1}{tan x}= \frac{tanx}{secx+1}

Required

Prove

Multiply the right-hand side by \frac{secx + 1}{secx + 1}

\frac{secx-1}{tan x} * \frac{secx + 1}{secx + 1}= \frac{tanx}{secx+1}

Apply difference of two squares on the numerator

\frac{sec^2 x - 1}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}

In trigonometry:

tan^2x = sec^2x - 1

So, we have:

\frac{tan^2 x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}

\frac{tan x * tan x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}

tan x cancels out

\frac{tan x}{secx + 1} =\frac{tanx}{secx+1}

<em>Proved</em>

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50 points!!
timurjin [86]

Answer:

y < -8

y > 4

Step-by-step explanation:

Absolute Value Inequality entered :

     |y+2|>6

Step by step solution :
Step 1: Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered

     |y+2| > 6

Step 2: Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |y+2|

For the Negative case we'll use -(y+2)

For the Positive case we'll use (y+2)

Step 3: Solve the Negative Case

     -(y+2) > 6

    Multiply

     -y-2 > 6

    Rearrange and Add up

     -y > 8

    Multiply both sides by (-1)

    Remember to flip the inequality sign

     y < -8

    Which is the solution for the Negative Case

Step 4: Solve the Positive Case

     (y+2) > 6

    Rearrange and Add up

     y > 4

    Which is the solution for the Positive Case

Step 5:

Wrap up the solution

 y < -8

 y > 4

Solutions in Interval Notation

   (-∞,-8)

   (4,+∞)

Solutions on the Number Line

 

Two solutions were found :

 y > 4

 y < -8

6 0
2 years ago
I neeeeddddd one moreeeee
Vadim26 [7]
Slope= 1
Y= 12
Equation= y = x + 12
3 0
2 years ago
Read 2 more answers
PLZ HELP 25 POINTS AND WILL MARK BRAINLIEST <br><br><br> Divide 3/4 ÷ 1/8 = ____.
faust18 [17]

Answer:

6

Step-by-step explanation:

3/4 ÷ 1/8

Copy dot flip

3/4 * 8/1

Rewriting

3/1 * 8/4

3/1 * 2/1

6

3 0
3 years ago
Read 2 more answers
Which of the following is equivalent to the equation -5(3x -8 )= -45 ?
Elan Coil [88]
Distributive property is
a(b+c)=ab+ac so
first, distribute
remember than (-) times (-)=(+)
-5(3x-8)=(-5)(3x)+(-5)(-8)=-15x+(+40)=-15x+40

so it is -15x+40=-45

the answe ris B
4 0
3 years ago
Find the sum of the following series. Round to the nearest hundredth if necessary,
Aneli [31]

Answer:

sum =   \frac{a( {r}^{n - 1} )}{r - 1}   \\  : but \: l = a( {r}^{n - 1} ) \\ 49152 = 3( {2}^{n - 1} ) \\ 16384 =  {2}^{n - 1}  \\  {2}^{n}  = 32768 \\  {2}^{n}  =  {2}^{15}  \\ n = 15 \\  \therefore \: sum =  \frac{3(2 {}^{15 - 1}) }{15 - 1}  \\  =  \frac{49152}{14}  \\  = 3510.9

3 0
3 years ago
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