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AnnyKZ [126]
3 years ago
6

I need help solving this trig problem w/ identites.

Mathematics
1 answer:
Charra [1.4K]3 years ago
3 0
\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad sec(\theta)=\cfrac{1}{cos(\theta)}
\\\\
-------------------------------

\bf \cfrac{1}{sin(x)-1}+\cfrac{1}{sin(x)+1}\implies \cfrac{sin(x)+1~~+~~sin(x)-1}{[sin(x)-1][sin(x)+1]}
\\\\\\
\cfrac{2sin(x)}{\stackrel{\textit{difference of squares}}{sin^2(x)-1^2}}\implies \cfrac{2sin(x)}{sin^2(x)-1}\implies \cfrac{2sin(x)}{-[~1-sin^2(x)~]}
\\\\\\
\cfrac{2sin(x)}{-[cos^2(x)]}\implies -2\cdot \cfrac{sin(x)}{cos(x)}\cdot \cfrac{1}{cos(x)}\implies -2tan(x)sec(x)
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Ilia_Sergeevich [38]

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Answer:

  x = 8/7

Step-by-step explanation:

  .2(.7x-5)+0.2=1.4(x-1.6) . . . . given

Eliminating parentheses, we have ...

  0.14x -1 +0.2 = 1.4x -2.24

  1.44 = 1.26x . . . . . . . add 2.24-0.14x to both sides

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  x = 8/7 . . . . . . . . . . .simplify the fraction

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As a repeating decimal, the value of x is ...

  x=1.\overline{142857}

However, the notation 1.(142857) is usually reserved for the case where the contents of parentheses are being multiplied by the factor in front. You would need to consult your instructions to see how the decimal version of the answer should be entered. (Quite often, rounding is suggested.)

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<em>Additional comment</em>

The equation in the text of your question is different from the one in the picture. We have answered for the one in the picture. The text asks for the solution of a quadratic. Those two solutions are approximately 1.085 and 16.057.

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Your friend is trying to see if you can guess the two numbers she secretly has written on her paper. Your friend tells you that
DaniilM [7]

Hello,

First we work out the equations:

x + y =62 will be the first equation.

2x= y +13 is the second equation.

We can first rewrite the second equation as 2x – y =13.

So we have:

x + y = 62

2x –y =13

KEEP IN MIND: With y being positive in one of the equations and negative in the other, we can combine the equations to quickly eliminate y and solve for x.

x + y = 62

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3x = 75 divide both sides by 3 to get x.

x = 25

Now that we have x we can substitute the value for x, 25.

25 + y = 62 we can subtract 25 from both sides to get y.

y = 62- 25

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