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kirill115 [55]
3 years ago
9

Which of the following would be an acceptable first step in simplifying the expression sin x/ 1-cos x

Mathematics
2 answers:
RideAnS [48]3 years ago
6 0

the question does not present the options, but this does not interfere with the resolution


we have

sin x/ (1-cos x)


we know that

sin²x+cos²x=1-----------> sin²x=1-cos²x

and

difference of squares

(a+b)*(a-b)=a²-b²

so

The idea is to make the difference of squares (1-cos²x)in denominator.so

multiply the expression by (1+cos x)/(1+cos x)

[sin x/ (1-cos x)]*[(1+cos x)/(1+cos x)]=[sin x*(1+cos x)]/[ (1-cos x)/(1+cos x)]

=[sin x*(1+cos x)]/[ (1-cos²x)]

=[sin x*(1+cos x)]/[ sin²x]

=(1+cos x)/sin x

=(1/sin x)+(cos x/sin x)

=csc x+cot x


therefore


the answer is

the first step is multiply the expression by (1+cos x)/(1+cos x)

Ray Of Light [21]3 years ago
6 0

Answer:

multiply expression by (1+cos x)/(1+cos x)

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Then, we use direct substitution:
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I don’t know how to do this. Can you help please help me ?
N76 [4]

Answer:

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  • cos = -1/2
  • tan = √3
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  • csc = (-2/3)√3
  • cot = (√3)/3

Step-by-step explanation:

See the attached picture for a drawing of the angle and its terminal point coordinates. Those are (cos(4π/3), sin(4π/3)), so we have the following trig function values:

  sin(4π/3) = -√3/2

  cos(4π/3) = -1/2

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  sec(4π/3) = 1/cos = -2

  csc(4π/3) = 1/sin = -(2√3)/3

  cot(4π/3) = 1/tan = (√3)/3

_____

<em>Additional comment</em>

It helps to know that 1/√a = (√a)/a. This lets you write the ratios with a rational denominator in each case.

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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<u>Let me define the each terms.</u>

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